x2-5x-5=15-2x

Solution for x2-5x-5=15-2x equation:

x2-5x-5=15-2x

We move all terms to the left:

x2-5x-5-(15-2x)=0

We add all the numbers together, and all the variables

x2-5x-(-2x+15)-5=0

We add all the numbers together, and all the variables

x^2-5x-(-2x+15)-5=0

We get rid of parentheses

x^2-5x+2x-15-5=0

We add all the numbers together, and all the variables

x^2-3x-20=0

a = 1; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·1·(-20)
Δ = 89
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{-(-3)-\sqrt{89}}{2*1}=\frac{3-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*1}=\frac{3+\sqrt{89}}{2}
$