2x^2+1=76

Solution for 2x^2+1=76 equation:

2x^2+1=76

We move all terms to the left:

2x^2+1-(76)=0

We add all the numbers together, and all the variables

2x^2-75=0

a = 2; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·2·(-75)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*2}=\frac{0-10\sqrt{6}}{4}
=-\frac{10\sqrt{6}}{4}
=-\frac{5\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*2}=\frac{0+10\sqrt{6}}{4}
=\frac{10\sqrt{6}}{4}
=\frac{5\sqrt{6}}{2}
$