x^2=28x^2+140x+165

Solution for x^2=28x^2+140x+165 equation:

x^2=28x^2+140x+165

We move all terms to the left:

x^2-(28x^2+140x+165)=0

We get rid of parentheses

x^2-28x^2-140x-165=0

We add all the numbers together, and all the variables

-27x^2-140x-165=0

a = -27; b = -140; c = -165;
Δ = b2-4ac
Δ = -1402-4·(-27)·(-165)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{445}}{2*-27}=\frac{140-2\sqrt{445}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{445}}{2*-27}=\frac{140+2\sqrt{445}}{-54}
$