(2x+3)(-4x-2)+2x=6(4x-6)+34

Solution for (2x+3)(-4x-2)+2x=6(4x-6)+34 equation:

(2x+3)(-4x-2)+2x=6(4x-6)+34

We move all terms to the left:

(2x+3)(-4x-2)+2x-(6(4x-6)+34)=0

We add all the numbers together, and all the variables

2x+(2x+3)(-4x-2)-(6(4x-6)+34)=0

We multiply parentheses ..

(-8x^2-4x-12x-6)+2x-(6(4x-6)+34)=0


We calculate terms in parentheses: -(6(4x-6)+34), so:

6(4x-6)+34

We multiply parentheses

24x-36+34

We add all the numbers together, and all the variables

24x-2

Back to the equation:

-(24x-2)


We get rid of parentheses

-8x^2-4x-12x+2x-24x-6+2=0

We add all the numbers together, and all the variables

-8x^2-38x-4=0

a = -8; b = -38; c = -4;
Δ = b2-4ac
Δ = -382-4·(-8)·(-4)
Δ = 1316
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:

$\sqrt{\Delta}=\sqrt{1316}=\sqrt{4*329}=\sqrt{4}*\sqrt{329}=2\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{329}}{2*-8}=\frac{38-2\sqrt{329}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{329}}{2*-8}=\frac{38+2\sqrt{329}}{-16}
$