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X^2-18X-4=02
We move all terms to the left:
X^2-18X-4-(02)=0
We add all the numbers together, and all the variables
X^2-18X-6=0
a = 1; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·1·(-6)
Δ = 348
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{87}}{2*1}=\frac{18-2\sqrt{87}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{87}}{2*1}=\frac{18+2\sqrt{87}}{2} $
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