120=2b^2-14b

Solution for 120=2b^2-14b equation:

120=2b^2-14b

We move all terms to the left:

120-(2b^2-14b)=0

We get rid of parentheses

-2b^2+14b+120=0

a = -2; b = 14; c = +120;
Δ = b2-4ac
Δ = 142-4·(-2)·120
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*-2}=\frac{-48}{-4}
=+12
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*-2}=\frac{20}{-4}
=-5
$