312(2x)=(2x^2)+(2x)

Solution for 312(2x)=(2x^2)+(2x) equation:

312(2x)=(2x^2)+(2x)

We move all terms to the left:

312(2x)-((2x^2)+(2x))=0

We get rid of parentheses

-2x^2+3122x-2x=0

We add all the numbers together, and all the variables

-2x^2+3120x=0

a = -2; b = 3120; c = 0;
Δ = b2-4ac
Δ = 31202-4·(-2)·0
Δ = 9734400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9734400}=3120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3120)-3120}{2*-2}=\frac{-6240}{-4}
=+1560
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3120)+3120}{2*-2}=\frac{0}{-4}
=0
$