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8x+24+3x(x+3)=4x(2)+12x
We move all terms to the left:
8x+24+3x(x+3)-(4x(2)+12x)=0
We add all the numbers together, and all the variables
-(+4x^2+12x)+8x+3x(x+3)+24=0
We multiply parentheses
-(+4x^2+12x)+3x^2+8x+9x+24=0
We get rid of parentheses
-4x^2+3x^2-12x+8x+9x+24=0
We add all the numbers together, and all the variables
-1x^2+5x+24=0
a = -1; b = 5; c = +24;
Δ = b2-4ac
Δ = 52-4·(-1)·24
Δ = 121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-1}=\frac{-16}{-2} =+8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-1}=\frac{6}{-2} =-3 $
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