2x2-78=42

Solution for 2x2-78=42 equation:

2x^2-78=42

We move all terms to the left:

2x^2-78-(42)=0

We add all the numbers together, and all the variables

2x^2-120=0

a = 2; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·2·(-120)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*2}=\frac{0-8\sqrt{15}}{4}
=-\frac{8\sqrt{15}}{4}
=-2\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*2}=\frac{0+8\sqrt{15}}{4}
=\frac{8\sqrt{15}}{4}
=2\sqrt{15}
$