16x^2=90-180x+9x^2

Solution for 16x^2=90-180x+9x^2 equation:

16x^2=90-180x+9x^2

We move all terms to the left:

16x^2-(90-180x+9x^2)=0

We get rid of parentheses

16x^2-9x^2+180x-90=0

We add all the numbers together, and all the variables

7x^2+180x-90=0

a = 7; b = 180; c = -90;
Δ = b2-4ac
Δ = 1802-4·7·(-90)
Δ = 34920
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:

$\sqrt{\Delta}=\sqrt{34920}=\sqrt{36*970}=\sqrt{36}*\sqrt{970}=6\sqrt{970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{970}}{2*7}=\frac{-180-6\sqrt{970}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{970}}{2*7}=\frac{-180+6\sqrt{970}}{14}
$