2x^2+51=172

Solution for 2x^2+51=172 equation:

2x^2+51=172

We move all terms to the left:

2x^2+51-(172)=0

We add all the numbers together, and all the variables

2x^2-121=0

a = 2; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·2·(-121)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*2}=\frac{0-22\sqrt{2}}{4}
=-\frac{22\sqrt{2}}{4}
=-\frac{11\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*2}=\frac{0+22\sqrt{2}}{4}
=\frac{22\sqrt{2}}{4}
=\frac{11\sqrt{2}}{2}
$