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5x+60=x^2+10
We move all terms to the left:
5x+60-(x^2+10)=0
We get rid of parentheses
-x^2+5x-10+60=0
We add all the numbers together, and all the variables
-1x^2+5x+50=0
a = -1; b = 5; c = +50;
Δ = b2-4ac
Δ = 52-4·(-1)·50
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*-1}=\frac{-20}{-2} =+10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*-1}=\frac{10}{-2} =-5 $
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