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x(x+3)+5(x+3)=x+3x+5x+15
We move all terms to the left:
x(x+3)+5(x+3)-(x+3x+5x+15)=0
We add all the numbers together, and all the variables
x(x+3)+5(x+3)-(9x+15)=0
We multiply parentheses
x^2+3x+5x-(9x+15)+15=0
We get rid of parentheses
x^2+3x+5x-9x-15+15=0
We add all the numbers together, and all the variables
x^2-1x=0
a = 1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·1·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*1}=\frac{0}{2} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*1}=\frac{2}{2} =1 $
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