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x^2+15x=5x-24
We move all terms to the left:
x^2+15x-(5x-24)=0
We get rid of parentheses
x^2+15x-5x+24=0
We add all the numbers together, and all the variables
x^2+10x+24=0
a = 1; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·1·24
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*1}=\frac{-12}{2} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*1}=\frac{-8}{2} =-4 $
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