16u^2-8u+1=36u^2-180u+225

Solution for 16u^2-8u+1=36u^2-180u+225 equation:

16u^2-8u+1=36u^2-180u+225

We move all terms to the left:

16u^2-8u+1-(36u^2-180u+225)=0

We get rid of parentheses

16u^2-36u^2-8u+180u-225+1=0

We add all the numbers together, and all the variables

-20u^2+172u-224=0

a = -20; b = 172; c = -224;
Δ = b2-4ac
Δ = 1722-4·(-20)·(-224)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172)-108}{2*-20}=\frac{-280}{-40}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172)+108}{2*-20}=\frac{-64}{-40}
=1+3/5
$