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6x^2-70x-165=0
a = 6; b = -70; c = -165;
Δ = b2-4ac
Δ = -702-4·6·(-165)
Δ = 8860
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8860}=\sqrt{4*2215}=\sqrt{4}*\sqrt{2215}=2\sqrt{2215}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{2215}}{2*6}=\frac{70-2\sqrt{2215}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{2215}}{2*6}=\frac{70+2\sqrt{2215}}{12} $
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