5u^2=3u+6

Solution for 5u^2=3u+6 equation:

5u^2=3u+6

We move all terms to the left:

5u^2-(3u+6)=0

We get rid of parentheses

5u^2-3u-6=0

a = 5; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·5·(-6)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{129}}{2*5}=\frac{3-\sqrt{129}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*5}=\frac{3+\sqrt{129}}{10}
$