(x+9)(2x)=90

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Solution for (x+9)(2x)=90 equation:



(x+9)(2x)=90
We move all terms to the left:
(x+9)(2x)-(90)=0
We multiply parentheses
2x^2+18x-90=0
a = 2; b = 18; c = -90;
Δ = b2-4ac
Δ = 182-4·2·(-90)
Δ = 1044
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:
$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{29}}{2*2}=\frac{-18-6\sqrt{29}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{29}}{2*2}=\frac{-18+6\sqrt{29}}{4} $

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