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-6x(3x+2)=2x-5-20x-7
We move all terms to the left:
-6x(3x+2)-(2x-5-20x-7)=0
We add all the numbers together, and all the variables
-6x(3x+2)-(-18x-12)=0
We multiply parentheses
-18x^2-12x-(-18x-12)=0
We get rid of parentheses
-18x^2-12x+18x+12=0
We add all the numbers together, and all the variables
-18x^2+6x+12=0
a = -18; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-18)·12
Δ = 900
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{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*-18}=\frac{-36}{-36} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*-18}=\frac{24}{-36} =-2/3 $
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