2u^2+21u=-27

Solution for 2u^2+21u=-27 equation:

2u^2+21u=-27

We move all terms to the left:

2u^2+21u-(-27)=0

We add all the numbers together, and all the variables

2u^2+21u+27=0

a = 2; b = 21; c = +27;
Δ = b2-4ac
Δ = 212-4·2·27
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*2}=\frac{-36}{4}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*2}=\frac{-6}{4}
=-1+1/2
$