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6x+60=x^2-5x
We move all terms to the left:
6x+60-(x^2-5x)=0
We get rid of parentheses
-x^2+6x+5x+60=0
We add all the numbers together, and all the variables
-1x^2+11x+60=0
a = -1; b = 11; c = +60;
Δ = b2-4ac
Δ = 112-4·(-1)·60
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*-1}=\frac{-30}{-2} =+15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*-1}=\frac{8}{-2} =-4 $
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