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9x-x(x-4)=-52
We move all terms to the left:
9x-x(x-4)-(-52)=0
We add all the numbers together, and all the variables
9x-x(x-4)+52=0
We multiply parentheses
-x^2+9x+4x+52=0
We add all the numbers together, and all the variables
-1x^2+13x+52=0
a = -1; b = 13; c = +52;
Δ = b2-4ac
Δ = 132-4·(-1)·52
Δ = 377
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{-(13)-\sqrt{377}}{2*-1}=\frac{-13-\sqrt{377}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{377}}{2*-1}=\frac{-13+\sqrt{377}}{-2} $
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