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18x^2-21x-154=0
a = 18; b = -21; c = -154;
Δ = b2-4ac
Δ = -212-4·18·(-154)
Δ = 11529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11529}=\sqrt{9*1281}=\sqrt{9}*\sqrt{1281}=3\sqrt{1281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{1281}}{2*18}=\frac{21-3\sqrt{1281}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{1281}}{2*18}=\frac{21+3\sqrt{1281}}{36} $
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