(2x+15)(2x-33)=2x

Solution for (2x+15)(2x-33)=2x equation:

(2x+15)(2x-33)=2x

We move all terms to the left:

(2x+15)(2x-33)-(2x)=0

We add all the numbers together, and all the variables

-2x+(2x+15)(2x-33)=0

We multiply parentheses ..

(+4x^2-66x+30x-495)-2x=0

We get rid of parentheses

4x^2-66x+30x-2x-495=0

We add all the numbers together, and all the variables

4x^2-38x-495=0

a = 4; b = -38; c = -495;
Δ = b2-4ac
Δ = -382-4·4·(-495)
Δ = 9364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9364}=\sqrt{4*2341}=\sqrt{4}*\sqrt{2341}=2\sqrt{2341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{2341}}{2*4}=\frac{38-2\sqrt{2341}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{2341}}{2*4}=\frac{38+2\sqrt{2341}}{8}
$