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-11x^2+4x=-18
We move all terms to the left:
-11x^2+4x-(-18)=0
We add all the numbers together, and all the variables
-11x^2+4x+18=0
a = -11; b = 4; c = +18;
Δ = b2-4ac
Δ = 42-4·(-11)·18
Δ = 808
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{202}}{2*-11}=\frac{-4-2\sqrt{202}}{-22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{202}}{2*-11}=\frac{-4+2\sqrt{202}}{-22} $
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