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(13+x)x=6
We move all terms to the left:
(13+x)x-(6)=0
We add all the numbers together, and all the variables
(x+13)x-6=0
We multiply parentheses
x^2+13x-6=0
a = 1; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·1·(-6)
Δ = 193
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{193}}{2*1}=\frac{-13-\sqrt{193}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{193}}{2*1}=\frac{-13+\sqrt{193}}{2} $
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