Question

4x^2 = 92 + 7x solve the equation using the guadratic formula, show all work

Answer 1

$4x^2=92+7x\ \ \ \ |-4x^2\\\\-4x^2+7x+92=0\\\\a=-4;\ b=7;\ c=92\\\\b^2-4ac=7^2-4\cdot(-4)\cdot92=49+1472=1521\\\\\sqrt{b^2-4ac}=\sqrt{1521}=39\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_1=\dfrac{-7-39}{2\cdot(-4)}=\dfrac{-46}{-8}=\dfrac{23}{4}\\\\x_2=\dfrac{-7+39}{2\cdot(-4)}=\dfrac{32}{-8}=-4$


$\text{Answer:}\ A.\ \left\{\dfrac{23}{4};\ -4\right\}$