(2x^2-7)/3=13

Solution for (2x^2-7)/3=13 equation:

(2x^2-7)/3=13

We move all terms to the left:

(2x^2-7)/3-(13)=0

We multiply all the terms by the denominator


(2x^2-7)-13*3=0

We add all the numbers together, and all the variables

(2x^2-7)-39=0

We get rid of parentheses

2x^2-7-39=0

We add all the numbers together, and all the variables

2x^2-46=0

a = 2; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·2·(-46)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{23}}{2*2}=\frac{0-4\sqrt{23}}{4}
=-\frac{4\sqrt{23}}{4}
=-\sqrt{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{23}}{2*2}=\frac{0+4\sqrt{23}}{4}
=\frac{4\sqrt{23}}{4}
=\sqrt{23}
$