2x^2=9x+126

Solution for 2x^2=9x+126 equation:

2x^2=9x+126

We move all terms to the left:

2x^2-(9x+126)=0

We get rid of parentheses

2x^2-9x-126=0

a = 2; b = -9; c = -126;
Δ = b2-4ac
Δ = -92-4·2·(-126)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*2}=\frac{42}{4}
=10+1/2
$