7x^2/3=12

Solution for 7x^2/3=12 equation:

7x^2/3=12

We move all terms to the left:

7x^2/3-(12)=0

We multiply all the terms by the denominator


7x^2-12*3=0

We add all the numbers together, and all the variables

7x^2-36=0

a = 7; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·7·(-36)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*7}=\frac{0-12\sqrt{7}}{14}
=-\frac{12\sqrt{7}}{14}
=-\frac{6\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*7}=\frac{0+12\sqrt{7}}{14}
=\frac{12\sqrt{7}}{14}
=\frac{6\sqrt{7}}{7}
$