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x^2+13x-17=6x-12
We move all terms to the left:
x^2+13x-17-(6x-12)=0
We get rid of parentheses
x^2+13x-6x+12-17=0
We add all the numbers together, and all the variables
x^2+7x-5=0
a = 1; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·1·(-5)
Δ = 69
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{-(7)-\sqrt{69}}{2*1}=\frac{-7-\sqrt{69}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*1}=\frac{-7+\sqrt{69}}{2} $
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