(5x^2+32)+(7x^2)=180

Solution for (5x^2+32)+(7x^2)=180 equation:

(5x^2+32)+(7x^2)=180

We move all terms to the left:

(5x^2+32)+(7x^2)-(180)=0

determiningTheFunctionDomain
7x^2+(5x^2+32)-180=0

We get rid of parentheses

7x^2+5x^2+32-180=0

We add all the numbers together, and all the variables

12x^2-148=0

a = 12; b = 0; c = -148;
Δ = b2-4ac
Δ = 02-4·12·(-148)
Δ = 7104
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:

$\sqrt{\Delta}=\sqrt{7104}=\sqrt{64*111}=\sqrt{64}*\sqrt{111}=8\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{111}}{2*12}=\frac{0-8\sqrt{111}}{24}
=-\frac{8\sqrt{111}}{24}
=-\frac{\sqrt{111}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{111}}{2*12}=\frac{0+8\sqrt{111}}{24}
=\frac{8\sqrt{111}}{24}
=\frac{\sqrt{111}}{3}
$