2x^2-5x+130=180

Solution for 2x^2-5x+130=180 equation:

2x^2-5x+130=180

We move all terms to the left:

2x^2-5x+130-(180)=0

We add all the numbers together, and all the variables

2x^2-5x-50=0

a = 2; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·2·(-50)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{17}}{2*2}=\frac{5-5\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{17}}{2*2}=\frac{5+5\sqrt{17}}{4}
$