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18=6x+x(x-13)
We move all terms to the left:
18-(6x+x(x-13))=0
We calculate terms in parentheses: -(6x+x(x-13)), so:We get rid of parentheses
6x+x(x-13)
We multiply parentheses
x^2+6x-13x
We add all the numbers together, and all the variables
x^2-7x
Back to the equation:
-(x^2-7x)
-x^2+7x+18=0
We add all the numbers together, and all the variables
-1x^2+7x+18=0
a = -1; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-1)·18
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-1}=\frac{-18}{-2} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-1}=\frac{4}{-2} =-2 $
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