(4u^2+4u-80)/(u^2-12u+32)=0

Solution for (4u^2+4u-80)/(u^2-12u+32)=0 equation:

(4u^2+4u-80)/(u^2-12u+32)=0


Domain of the equation: (u^2-12u+32)!=0

We move all terms containing u to the left, all other terms to the right

u^2-12u!=-32

u∈R


We multiply all the terms by the denominator


(4u^2+4u-80)=0

We get rid of parentheses

4u^2+4u-80=0

a = 4; b = 4; c = -80;
Δ = b2-4ac
Δ = 42-4·4·(-80)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-36}{2*4}=\frac{-40}{8}
=-5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+36}{2*4}=\frac{32}{8}
=4
$