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x^2+12x-13x=10x+2
We move all terms to the left:
x^2+12x-13x-(10x+2)=0
We add all the numbers together, and all the variables
x^2-1x-(10x+2)=0
We get rid of parentheses
x^2-1x-10x-2=0
We add all the numbers together, and all the variables
x^2-11x-2=0
a = 1; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·1·(-2)
Δ = 129
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{129}}{2*1}=\frac{11-\sqrt{129}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{129}}{2*1}=\frac{11+\sqrt{129}}{2} $
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