Question

Select the two values of x that are roots of this equation 2x-3=-5x^2

Answer 1

$\bold{Answer}$

$\boxed{\bold{X \ = \ -1, \ X \ = \ \frac{3}{5} }}$

$\bold{Explanation}$

• $\bold{Find \ Two \ Values \ Of \ X: \ 2x-3=-5x^2}$

$\bold{-------------------}$

• $\bold{Switch \ Sides}$

$\bold{-5x^2=2x-3}$

• $\bold{Add \ 3 \ To \ Both \ Sides}$

$\bold{-5x^2+3=2x-3+3}$

• $\bold{Simplify}$

$\bold{-5x^2+3=2x}$

• $\bold{Subtract \ 2x \ From \ Both \ Sides}$

$\bold{-5x^2+3-2x=2x-2x}$

• $\bold{Simplify}$

$\bold{-5x^2-2x+3=0}$

• $\bold{Solve \ With \ The \ Quadratic \ Formula}$
• $\bold{For \ The \ Quadratic \ Form \ For \ ax^2+bx+c=0 \ The \ Solutions \ Are \ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$
• $\bold{For \ A \ =-5,\:b=-2,\:c=3:\quad x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\left(-5\right)3}}{2\left(-5\right)}}$

$\bold{\frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ -1}$

$\bold{\frac{-\left(-2\right)-\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ \frac{3}{5} }$

• $\bold{Solutions}$

$\bold{x=-1,\:x=\frac{3}{5}}$

$\boxed{\bold{Eclipsed}}$