20u^2+3u=5u^2+5u+1

Solution for 20u^2+3u=5u^2+5u+1 equation:

20u^2+3u=5u^2+5u+1

We move all terms to the left:

20u^2+3u-(5u^2+5u+1)=0

We get rid of parentheses

20u^2-5u^2+3u-5u-1=0

We add all the numbers together, and all the variables

15u^2-2u-1=0

a = 15; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·15·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*15}=\frac{-6}{30}
=-1/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*15}=\frac{10}{30}
=1/3
$