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(x+4)(3x+6)+(5-10x)(3x+6)=6x+12
We move all terms to the left:
(x+4)(3x+6)+(5-10x)(3x+6)-(6x+12)=0
We add all the numbers together, and all the variables
(x+4)(3x+6)+(-10x+5)(3x+6)-(6x+12)=0
We get rid of parentheses
(x+4)(3x+6)+(-10x+5)(3x+6)-6x-12=0
We multiply parentheses ..
(+3x^2+6x+12x+24)+(-10x+5)(3x+6)-6x-12=0
We add all the numbers together, and all the variables
(+3x^2+6x+12x+24)-6x+(-10x+5)(3x+6)-12=0
We get rid of parentheses
3x^2+6x+12x-6x+(-10x+5)(3x+6)+24-12=0
We multiply parentheses ..
3x^2+(-30x^2-60x+15x+30)+6x+12x-6x+24-12=0
We add all the numbers together, and all the variables
3x^2+(-30x^2-60x+15x+30)+12x+12=0
We get rid of parentheses
3x^2-30x^2-60x+15x+12x+30+12=0
We add all the numbers together, and all the variables
-27x^2-33x+42=0
a = -27; b = -33; c = +42;
Δ = b2-4ac
Δ = -332-4·(-27)·42
Δ = 5625
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{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-75}{2*-27}=\frac{-42}{-54} =7/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+75}{2*-27}=\frac{108}{-54} =-2 $
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