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4x(x+8)=-24
We move all terms to the left:
4x(x+8)-(-24)=0
We add all the numbers together, and all the variables
4x(x+8)+24=0
We multiply parentheses
4x^2+32x+24=0
a = 4; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·4·24
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{10}}{2*4}=\frac{-32-8\sqrt{10}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{10}}{2*4}=\frac{-32+8\sqrt{10}}{8} $
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