4u^2+12u+54u=0

Solution for 4u^2+12u+54u=0 equation:

4u^2+12u+54u=0

We add all the numbers together, and all the variables

4u^2+66u=0

a = 4; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·4·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*4}=\frac{-132}{8}
=-16+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*4}=\frac{0}{8}
=0
$