4u^2=-11u-6

Solution for 4u^2=-11u-6 equation:

4u^2=-11u-6

We move all terms to the left:

4u^2-(-11u-6)=0

We get rid of parentheses

4u^2+11u+6=0

a = 4; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·4·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*4}=\frac{-16}{8}
=-2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*4}=\frac{-6}{8}
=-3/4
$