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2x(x+12)=3x+24
We move all terms to the left:
2x(x+12)-(3x+24)=0
We multiply parentheses
2x^2+24x-(3x+24)=0
We get rid of parentheses
2x^2+24x-3x-24=0
We add all the numbers together, and all the variables
2x^2+21x-24=0
a = 2; b = 21; c = -24;
Δ = b2-4ac
Δ = 212-4·2·(-24)
Δ = 633
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{633}}{2*2}=\frac{-21-\sqrt{633}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{633}}{2*2}=\frac{-21+\sqrt{633}}{4} $
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