x^2-5x+x^2-10x=50

Solution for x^2-5x+x^2-10x=50 equation:

x^2-5x+x^2-10x=50

We move all terms to the left:

x^2-5x+x^2-10x-(50)=0

We add all the numbers together, and all the variables

2x^2-15x-50=0

a = 2; b = -15; c = -50;
Δ = b2-4ac
Δ = -152-4·2·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-25}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+25}{2*2}=\frac{40}{4}
=10
$