2(x*x)-7x-6=120

Solution for 2(x*x)-7x-6=120 equation:

2(x*x)-7x-6=120

We move all terms to the left:

2(x*x)-7x-6-(120)=0

We add all the numbers together, and all the variables

2(+x*x)-7x-6-120=0

We add all the numbers together, and all the variables

-7x+2(+x*x)-126=0

We multiply parentheses

2x^2-7x-126=0

a = 2; b = -7; c = -126;
Δ = b2-4ac
Δ = -72-4·2·(-126)
Δ = 1057
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{1057}}{2*2}=\frac{7-\sqrt{1057}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1057}}{2*2}=\frac{7+\sqrt{1057}}{4}
$