2x(5x-1)-8x=3x+2

Solution for 2x(5x-1)-8x=3x+2 equation:

2x(5x-1)-8x=3x+2

We move all terms to the left:

2x(5x-1)-8x-(3x+2)=0

We add all the numbers together, and all the variables

-8x+2x(5x-1)-(3x+2)=0

We multiply parentheses

10x^2-8x-2x-(3x+2)=0

We get rid of parentheses

10x^2-8x-2x-3x-2=0

We add all the numbers together, and all the variables

10x^2-13x-2=0

a = 10; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·10·(-2)
Δ = 249
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{-(-13)-\sqrt{249}}{2*10}=\frac{13-\sqrt{249}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{249}}{2*10}=\frac{13+\sqrt{249}}{20}
$