5x(x-2)-2(4x-3)-(x+4)=-8

Solution for 5x(x-2)-2(4x-3)-(x+4)=-8 equation:

5x(x-2)-2(4x-3)-(x+4)=-8

We move all terms to the left:

5x(x-2)-2(4x-3)-(x+4)-(-8)=0

We add all the numbers together, and all the variables

5x(x-2)-2(4x-3)-(x+4)+8=0

We multiply parentheses

5x^2-10x-8x-(x+4)+6+8=0

We get rid of parentheses

5x^2-10x-8x-x-4+6+8=0

We add all the numbers together, and all the variables

5x^2-19x+10=0

a = 5; b = -19; c = +10;
Δ = b2-4ac
Δ = -192-4·5·10
Δ = 161
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{161}}{2*5}=\frac{19-\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{161}}{2*5}=\frac{19+\sqrt{161}}{10}
$