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6x(12-x)=3x-2
We move all terms to the left:
6x(12-x)-(3x-2)=0
We add all the numbers together, and all the variables
6x(-1x+12)-(3x-2)=0
We multiply parentheses
-6x^2+72x-(3x-2)=0
We get rid of parentheses
-6x^2+72x-3x+2=0
We add all the numbers together, and all the variables
-6x^2+69x+2=0
a = -6; b = 69; c = +2;
Δ = b2-4ac
Δ = 692-4·(-6)·2
Δ = 4809
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{-(69)-\sqrt{4809}}{2*-6}=\frac{-69-\sqrt{4809}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{4809}}{2*-6}=\frac{-69+\sqrt{4809}}{-12} $
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