(2x^2+7)+(61-x^2)+117=360

Solution for (2x^2+7)+(61-x^2)+117=360 equation:

(2x^2+7)+(61-x^2)+117=360

We move all terms to the left:

(2x^2+7)+(61-x^2)+117-(360)=0

We add all the numbers together, and all the variables

(61-x^2)+(2x^2+7)-243=0

We get rid of parentheses

-x^2+2x^2+61+7-243=0

We add all the numbers together, and all the variables

x^2-175=0

a = 1; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·1·(-175)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*1}=\frac{0-10\sqrt{7}}{2}
=-\frac{10\sqrt{7}}{2}
=-5\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*1}=\frac{0+10\sqrt{7}}{2}
=\frac{10\sqrt{7}}{2}
=5\sqrt{7}
$