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

Solution for 5x(x-1)-2(2x^2+7x)=-8 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x^2-4x^2-5x-14x+8=0

We add all the numbers together, and all the variables

x^2-19x+8=0

a = 1; b = -19; c = +8;
Δ = b2-4ac
Δ = -192-4·1·8
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{329}}{2*1}=\frac{19-\sqrt{329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{329}}{2*1}=\frac{19+\sqrt{329}}{2}
$