2x^2=7x+120

Solution for 2x^2=7x+120 equation:

2x^2=7x+120

We move all terms to the left:

2x^2-(7x+120)=0

We get rid of parentheses

2x^2-7x-120=0

a = 2; b = -7; c = -120;
Δ = b2-4ac
Δ = -72-4·2·(-120)
Δ = 1009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1009}}{2*2}=\frac{7-\sqrt{1009}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1009}}{2*2}=\frac{7+\sqrt{1009}}{4}
$