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2x(x+3)=24+15
We move all terms to the left:
2x(x+3)-(24+15)=0
We add all the numbers together, and all the variables
2x(x+3)-39=0
We multiply parentheses
2x^2+6x-39=0
a = 2; b = 6; c = -39;
Δ = b2-4ac
Δ = 62-4·2·(-39)
Δ = 348
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{87}}{2*2}=\frac{-6-2\sqrt{87}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{87}}{2*2}=\frac{-6+2\sqrt{87}}{4} $
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