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x^2-8x=6x-24
We move all terms to the left:
x^2-8x-(6x-24)=0
We get rid of parentheses
x^2-8x-6x+24=0
We add all the numbers together, and all the variables
x^2-14x+24=0
a = 1; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·1·24
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*1}=\frac{4}{2} =2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*1}=\frac{24}{2} =12 $
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