5x^2-10x-13=9x-9

Solution for 5x^2-10x-13=9x-9 equation:

5x^2-10x-13=9x-9

We move all terms to the left:

5x^2-10x-13-(9x-9)=0

We get rid of parentheses

5x^2-10x-9x+9-13=0

We add all the numbers together, and all the variables

5x^2-19x-4=0

a = 5; b = -19; c = -4;
Δ = b2-4ac
Δ = -192-4·5·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-21}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+21}{2*5}=\frac{40}{10}
=4
$