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4q(q+5)=-24
We move all terms to the left:
4q(q+5)-(-24)=0
We add all the numbers together, and all the variables
4q(q+5)+24=0
We multiply parentheses
4q^2+20q+24=0
a = 4; b = 20; c = +24;
Δ = b2-4ac
Δ = 202-4·4·24
Δ = 16
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}$$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{16}=4$$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*4}=\frac{-24}{8} =-3 $$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*4}=\frac{-16}{8} =-2 $
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