20x^2-130x=-20

Solution for 20x^2-130x=-20 equation:

20x^2-130x=-20

We move all terms to the left:

20x^2-130x-(-20)=0

We add all the numbers together, and all the variables

20x^2-130x+20=0

a = 20; b = -130; c = +20;
Δ = b2-4ac
Δ = -1302-4·20·20
Δ = 15300
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:

$\sqrt{\Delta}=\sqrt{15300}=\sqrt{900*17}=\sqrt{900}*\sqrt{17}=30\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-30\sqrt{17}}{2*20}=\frac{130-30\sqrt{17}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+30\sqrt{17}}{2*20}=\frac{130+30\sqrt{17}}{40}
$