2x^2-10x+130=180

Solution for 2x^2-10x+130=180 equation:

2x^2-10x+130=180

We move all terms to the left:

2x^2-10x+130-(180)=0

We add all the numbers together, and all the variables

2x^2-10x-50=0

a = 2; b = -10; c = -50;
Δ = b2-4ac
Δ = -102-4·2·(-50)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{5}}{2*2}=\frac{10-10\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{5}}{2*2}=\frac{10+10\sqrt{5}}{4}
$