5u^2-41u=-8

Solution for 5u^2-41u=-8 equation:

5u^2-41u=-8

We move all terms to the left:

5u^2-41u-(-8)=0

We add all the numbers together, and all the variables

5u^2-41u+8=0

a = 5; b = -41; c = +8;
Δ = b2-4ac
Δ = -412-4·5·8
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-39}{2*5}=\frac{2}{10}
=1/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+39}{2*5}=\frac{80}{10}
=8
$