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12x^2+18x=x+15
We move all terms to the left:
12x^2+18x-(x+15)=0
We get rid of parentheses
12x^2+18x-x-15=0
We add all the numbers together, and all the variables
12x^2+17x-15=0
a = 12; b = 17; c = -15;
Δ = b2-4ac
Δ = 172-4·12·(-15)
Δ = 1009
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{-(17)-\sqrt{1009}}{2*12}=\frac{-17-\sqrt{1009}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{1009}}{2*12}=\frac{-17+\sqrt{1009}}{24} $
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