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9x(x+10)=-99
We move all terms to the left:
9x(x+10)-(-99)=0
We add all the numbers together, and all the variables
9x(x+10)+99=0
We multiply parentheses
9x^2+90x+99=0
a = 9; b = 90; c = +99;
Δ = b2-4ac
Δ = 902-4·9·99
Δ = 4536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4536}=\sqrt{324*14}=\sqrt{324}*\sqrt{14}=18\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-18\sqrt{14}}{2*9}=\frac{-90-18\sqrt{14}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+18\sqrt{14}}{2*9}=\frac{-90+18\sqrt{14}}{18} $
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