-5x(2x-7)-x=2(x+2)-8

Solution for -5x(2x-7)-x=2(x+2)-8 equation:

-5x(2x-7)-x=2(x+2)-8

We move all terms to the left:

-5x(2x-7)-x-(2(x+2)-8)=0

We add all the numbers together, and all the variables

-1x-5x(2x-7)-(2(x+2)-8)=0

We multiply parentheses

-10x^2-1x+35x-(2(x+2)-8)=0


We calculate terms in parentheses: -(2(x+2)-8), so:

2(x+2)-8

We multiply parentheses

2x+4-8

We add all the numbers together, and all the variables

2x-4

Back to the equation:

-(2x-4)


We add all the numbers together, and all the variables

-10x^2+34x-(2x-4)=0

We get rid of parentheses

-10x^2+34x-2x+4=0

We add all the numbers together, and all the variables

-10x^2+32x+4=0

a = -10; b = 32; c = +4;
Δ = b2-4ac
Δ = 322-4·(-10)·4
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{74}}{2*-10}=\frac{-32-4\sqrt{74}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{74}}{2*-10}=\frac{-32+4\sqrt{74}}{-20}
$