5x^2-20x-8=2+3x

Solution for 5x^2-20x-8=2+3x equation:

5x^2-20x-8=2+3x

We move all terms to the left:

5x^2-20x-8-(2+3x)=0

We add all the numbers together, and all the variables

5x^2-20x-(3x+2)-8=0

We get rid of parentheses

5x^2-20x-3x-2-8=0

We add all the numbers together, and all the variables

5x^2-23x-10=0

a = 5; b = -23; c = -10;
Δ = b2-4ac
Δ = -232-4·5·(-10)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-27}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+27}{2*5}=\frac{50}{10}
=5
$