5x^2-20x-1=13x+13

Solution for 5x^2-20x-1=13x+13 equation:

5x^2-20x-1=13x+13

We move all terms to the left:

5x^2-20x-1-(13x+13)=0

We get rid of parentheses

5x^2-20x-13x-13-1=0

We add all the numbers together, and all the variables

5x^2-33x-14=0

a = 5; b = -33; c = -14;
Δ = b2-4ac
Δ = -332-4·5·(-14)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-37}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+37}{2*5}=\frac{70}{10}
=7
$