-3u^2+5u=-6

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

-3u^2+5u=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -3; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-3)·6
Δ = 97
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{-(5)-\sqrt{97}}{2*-3}=\frac{-5-\sqrt{97}}{-6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*-3}=\frac{-5+\sqrt{97}}{-6}
$