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18x^2+38x-11=0
a = 18; b = 38; c = -11;
Δ = b2-4ac
Δ = 382-4·18·(-11)
Δ = 2236
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2236}=\sqrt{4*559}=\sqrt{4}*\sqrt{559}=2\sqrt{559}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{559}}{2*18}=\frac{-38-2\sqrt{559}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{559}}{2*18}=\frac{-38+2\sqrt{559}}{36} $
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