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6x(6-2x)=18+5x
We move all terms to the left:
6x(6-2x)-(18+5x)=0
We add all the numbers together, and all the variables
6x(-2x+6)-(5x+18)=0
We multiply parentheses
-12x^2+36x-(5x+18)=0
We get rid of parentheses
-12x^2+36x-5x-18=0
We add all the numbers together, and all the variables
-12x^2+31x-18=0
a = -12; b = 31; c = -18;
Δ = b2-4ac
Δ = 312-4·(-12)·(-18)
Δ = 97
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{-(31)-\sqrt{97}}{2*-12}=\frac{-31-\sqrt{97}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{97}}{2*-12}=\frac{-31+\sqrt{97}}{-24} $
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