6x2=74

Solution for 6x2=74 equation:

6x^2=74

We move all terms to the left:

6x^2-(74)=0

a = 6; b = 0; c = -74;
Δ = b2-4ac
Δ = 02-4·6·(-74)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{111}}{2*6}=\frac{0-4\sqrt{111}}{12}
=-\frac{4\sqrt{111}}{12}
=-\frac{\sqrt{111}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{111}}{2*6}=\frac{0+4\sqrt{111}}{12}
=\frac{4\sqrt{111}}{12}
=\frac{\sqrt{111}}{3}
$