2a^2-52a+312=0

Solution for 2a^2-52a+312=0 equation:

2a^2-52a+312=0

a = 2; b = -52; c = +312;
Δ = b2-4ac
Δ = -522-4·2·312
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{13}}{2*2}=\frac{52-4\sqrt{13}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{13}}{2*2}=\frac{52+4\sqrt{13}}{4}
$