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101x^2-80x-705=0
a = 101; b = -80; c = -705;
Δ = b2-4ac
Δ = -802-4·101·(-705)
Δ = 291220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291220}=\sqrt{4*72805}=\sqrt{4}*\sqrt{72805}=2\sqrt{72805}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{72805}}{2*101}=\frac{80-2\sqrt{72805}}{202} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{72805}}{2*101}=\frac{80+2\sqrt{72805}}{202} $
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