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8x^2-186x-1830=0
a = 8; b = -186; c = -1830;
Δ = b2-4ac
Δ = -1862-4·8·(-1830)
Δ = 93156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{93156}=\sqrt{4*23289}=\sqrt{4}*\sqrt{23289}=2\sqrt{23289}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-2\sqrt{23289}}{2*8}=\frac{186-2\sqrt{23289}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+2\sqrt{23289}}{2*8}=\frac{186+2\sqrt{23289}}{16} $
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