36=4(q+54)q=

Solution for 36=4(q+54)q= equation:

36=4(q+54)q=

We move all terms to the left:

36-(4(q+54)q)=0


We calculate terms in parentheses: -(4(q+54)q), so:

4(q+54)q

We multiply parentheses

4q^2+216q

Back to the equation:

-(4q^2+216q)


We get rid of parentheses

-4q^2-216q+36=0

a = -4; b = -216; c = +36;
Δ = b2-4ac
Δ = -2162-4·(-4)·36
Δ = 47232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{47232}=\sqrt{576*82}=\sqrt{576}*\sqrt{82}=24\sqrt{82}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-24\sqrt{82}}{2*-4}=\frac{216-24\sqrt{82}}{-8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+24\sqrt{82}}{2*-4}=\frac{216+24\sqrt{82}}{-8}
$