Question

Given y= 2x squared - 10x find all the real values of x for which y = -3

Answer 1

$y=2 x^{2} -10x \\ -3=2 x^{2} -10x \\ 2 x^{2} -10x+3=0 \\ x=\frac{-b \pm \sqrt{ b^{2} -4ac} }{2a}, \ where \ a=2, \ b=-10, \ c=3$
Therefore,
$x=\frac{-(-10) \pm \sqrt{ (-10)^{2} -(4 \times 2 \times 3)} }{2 \times 2} \\ =\frac{10 \pm \sqrt{ 100 -24} }{4} \\ =\frac{10 \pm \sqrt{ 76} }{4} \\= \frac{10 + \sqrt{ 76} }{4} \ or \ \frac{10 - \sqrt{ 76} }{4} \\ =4.679 \ or \ 0.3206$