6+(7x2+5)2/2=180

Solution for 6+(7x2+5)2/2=180 equation:

6+(7x^2+5)2/2=180

We move all terms to the left:

6+(7x^2+5)2/2-(180)=0

We add all the numbers together, and all the variables

(7x^2+5)2/2-174=0

We multiply all the terms by the denominator


(7x^2+5)2-174*2=0

We add all the numbers together, and all the variables

(7x^2+5)2-348=0

We multiply parentheses

14x^2+10-348=0

We add all the numbers together, and all the variables

14x^2-338=0

a = 14; b = 0; c = -338;
Δ = b2-4ac
Δ = 02-4·14·(-338)
Δ = 18928
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:

$\sqrt{\Delta}=\sqrt{18928}=\sqrt{2704*7}=\sqrt{2704}*\sqrt{7}=52\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{7}}{2*14}=\frac{0-52\sqrt{7}}{28}
=-\frac{52\sqrt{7}}{28}
=-\frac{13\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{7}}{2*14}=\frac{0+52\sqrt{7}}{28}
=\frac{52\sqrt{7}}{28}
=\frac{13\sqrt{7}}{7}
$