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11x^2+8x=90
We move all terms to the left:
11x^2+8x-(90)=0
a = 11; b = 8; c = -90;
Δ = b2-4ac
Δ = 82-4·11·(-90)
Δ = 4024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4024}=\sqrt{4*1006}=\sqrt{4}*\sqrt{1006}=2\sqrt{1006}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{1006}}{2*11}=\frac{-8-2\sqrt{1006}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{1006}}{2*11}=\frac{-8+2\sqrt{1006}}{22} $
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