(2x^2+7)/3=26

Solution for (2x^2+7)/3=26 equation:

(2x^2+7)/3=26

We move all terms to the left:

(2x^2+7)/3-(26)=0

We multiply all the terms by the denominator


(2x^2+7)-26*3=0

We add all the numbers together, and all the variables

(2x^2+7)-78=0

We get rid of parentheses

2x^2+7-78=0

We add all the numbers together, and all the variables

2x^2-71=0

a = 2; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·2·(-71)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{142}}{2*2}=\frac{0-2\sqrt{142}}{4}
=-\frac{2\sqrt{142}}{4}
=-\frac{\sqrt{142}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{142}}{2*2}=\frac{0+2\sqrt{142}}{4}
=\frac{2\sqrt{142}}{4}
=\frac{\sqrt{142}}{2}
$