x^2+25+6x^2-10=180

Solution for x^2+25+6x^2-10=180 equation:

x^2+25+6x^2-10=180

We move all terms to the left:

x^2+25+6x^2-10-(180)=0

We add all the numbers together, and all the variables

7x^2-165=0

a = 7; b = 0; c = -165;
Δ = b2-4ac
Δ = 02-4·7·(-165)
Δ = 4620
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:

$\sqrt{\Delta}=\sqrt{4620}=\sqrt{4*1155}=\sqrt{4}*\sqrt{1155}=2\sqrt{1155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1155}}{2*7}=\frac{0-2\sqrt{1155}}{14}
=-\frac{2\sqrt{1155}}{14}
=-\frac{\sqrt{1155}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1155}}{2*7}=\frac{0+2\sqrt{1155}}{14}
=\frac{2\sqrt{1155}}{14}
=\frac{\sqrt{1155}}{7}
$