5x^2-50x+60=-5

Solution for 5x^2-50x+60=-5 equation:

5x^2-50x+60=-5

We move all terms to the left:

5x^2-50x+60-(-5)=0

We add all the numbers together, and all the variables

5x^2-50x+65=0

a = 5; b = -50; c = +65;
Δ = b2-4ac
Δ = -502-4·5·65
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20\sqrt{3}}{2*5}=\frac{50-20\sqrt{3}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20\sqrt{3}}{2*5}=\frac{50+20\sqrt{3}}{10}
$