(6x^2)/4=117

Solution for (6x^2)/4=117 equation:

(6x^2)/4=117

We move all terms to the left:

(6x^2)/4-(117)=0

We multiply all the terms by the denominator


6x^2-117*4=0

We add all the numbers together, and all the variables

6x^2-468=0

a = 6; b = 0; c = -468;
Δ = b2-4ac
Δ = 02-4·6·(-468)
Δ = 11232
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:

$\sqrt{\Delta}=\sqrt{11232}=\sqrt{144*78}=\sqrt{144}*\sqrt{78}=12\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{78}}{2*6}=\frac{0-12\sqrt{78}}{12}
=-\frac{12\sqrt{78}}{12}
=-\sqrt{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{78}}{2*6}=\frac{0+12\sqrt{78}}{12}
=\frac{12\sqrt{78}}{12}
=\sqrt{78}
$