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0=-x(x-9)+52
We move all terms to the left:
0-(-x(x-9)+52)=0
We add all the numbers together, and all the variables
-(-x(x-9)+52)=0
We calculate terms in parentheses: -(-x(x-9)+52), so:We get rid of parentheses
-x(x-9)+52
We multiply parentheses
-x^2+9x+52
We add all the numbers together, and all the variables
-1x^2+9x+52
Back to the equation:
-(-1x^2+9x+52)
1x^2-9x-52=0
We add all the numbers together, and all the variables
x^2-9x-52=0
a = 1; b = -9; c = -52;
Δ = b2-4ac
Δ = -92-4·1·(-52)
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-17}{2*1}=\frac{-8}{2} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+17}{2*1}=\frac{26}{2} =13 $
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