2x^2/3-7=91

Solution for 2x^2/3-7=91 equation:

2x^2/3-7=91

We move all terms to the left:

2x^2/3-7-(91)=0

We add all the numbers together, and all the variables

2x^2/3-98=0

We multiply all the terms by the denominator


2x^2-98*3=0

We add all the numbers together, and all the variables

2x^2-294=0

a = 2; b = 0; c = -294;
Δ = b2-4ac
Δ = 02-4·2·(-294)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{3}}{2*2}=\frac{0-28\sqrt{3}}{4}
=-\frac{28\sqrt{3}}{4}
=-7\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{3}}{2*2}=\frac{0+28\sqrt{3}}{4}
=\frac{28\sqrt{3}}{4}
=7\sqrt{3}
$