2x^2-84=170

Solution for 2x^2-84=170 equation:

2x^2-84=170

We move all terms to the left:

2x^2-84-(170)=0

We add all the numbers together, and all the variables

2x^2-254=0

a = 2; b = 0; c = -254;
Δ = b2-4ac
Δ = 02-4·2·(-254)
Δ = 2032
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:

$\sqrt{\Delta}=\sqrt{2032}=\sqrt{16*127}=\sqrt{16}*\sqrt{127}=4\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{127}}{2*2}=\frac{0-4\sqrt{127}}{4}
=-\frac{4\sqrt{127}}{4}
=-\sqrt{127}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{127}}{2*2}=\frac{0+4\sqrt{127}}{4}
=\frac{4\sqrt{127}}{4}
=\sqrt{127}
$