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(x-13)(x+3)=0x
We move all terms to the left:
(x-13)(x+3)-(0x)=0
We add all the numbers together, and all the variables
-1x+(x-13)(x+3)=0
We multiply parentheses ..
(+x^2+3x-13x-39)-1x=0
We get rid of parentheses
x^2+3x-13x-1x-39=0
We add all the numbers together, and all the variables
x^2-11x-39=0
a = 1; b = -11; c = -39;
Δ = b2-4ac
Δ = -112-4·1·(-39)
Δ = 277
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{277}}{2*1}=\frac{11-\sqrt{277}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{277}}{2*1}=\frac{11+\sqrt{277}}{2} $
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