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6x=x2-5x-12
We move all terms to the left:
6x-(x2-5x-12)=0
We add all the numbers together, and all the variables
-(+x^2-5x-12)+6x=0
We get rid of parentheses
-x^2+5x+6x+12=0
We add all the numbers together, and all the variables
-1x^2+11x+12=0
a = -1; b = 11; c = +12;
Δ = b2-4ac
Δ = 112-4·(-1)·12
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*-1}=\frac{-24}{-2} =+12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*-1}=\frac{2}{-2} =-1 $
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