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(10+x)x=90+x

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Solution for (10+x)x=90+x equation:



(10+x)x=90+x
We move all terms to the left:
(10+x)x-(90+x)=0
We add all the numbers together, and all the variables
(x+10)x-(x+90)=0
We multiply parentheses
x^2+10x-(x+90)=0
We get rid of parentheses
x^2+10x-x-90=0
We add all the numbers together, and all the variables
x^2+9x-90=0
a = 1; b = 9; c = -90;
Δ = b2-4ac
Δ = 92-4·1·(-90)
Δ = 441
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{441}=21
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*1}=\frac{-30}{2} =-15
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*1}=\frac{12}{2} =6

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