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5x-x(x-6)=-11
We move all terms to the left:
5x-x(x-6)-(-11)=0
We add all the numbers together, and all the variables
5x-x(x-6)+11=0
We multiply parentheses
-x^2+5x+6x+11=0
We add all the numbers together, and all the variables
-1x^2+11x+11=0
a = -1; b = 11; c = +11;
Δ = b2-4ac
Δ = 112-4·(-1)·11
Δ = 165
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{-(11)-\sqrt{165}}{2*-1}=\frac{-11-\sqrt{165}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{165}}{2*-1}=\frac{-11+\sqrt{165}}{-2} $
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