2x^2-10x+102=180

Solution for 2x^2-10x+102=180 equation:

2x^2-10x+102=180

We move all terms to the left:

2x^2-10x+102-(180)=0

We add all the numbers together, and all the variables

2x^2-10x-78=0

a = 2; b = -10; c = -78;
Δ = b2-4ac
Δ = -102-4·2·(-78)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{181}}{2*2}=\frac{10-2\sqrt{181}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{181}}{2*2}=\frac{10+2\sqrt{181}}{4}
$