2x^2+102=32x

Solution for 2x^2+102=32x equation:

2x^2+102=32x

We move all terms to the left:

2x^2+102-(32x)=0

a = 2; b = -32; c = +102;
Δ = b2-4ac
Δ = -322-4·2·102
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{13}}{2*2}=\frac{32-4\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{13}}{2*2}=\frac{32+4\sqrt{13}}{4}
$