2x^2-5=75

Solution for 2x^2-5=75 equation:

2x^2-5=75

We move all terms to the left:

2x^2-5-(75)=0

We add all the numbers together, and all the variables

2x^2-80=0

a = 2; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·2·(-80)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*2}=\frac{0-8\sqrt{10}}{4}
=-\frac{8\sqrt{10}}{4}
=-2\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*2}=\frac{0+8\sqrt{10}}{4}
=\frac{8\sqrt{10}}{4}
=2\sqrt{10}
$