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12x^2-175x-1500=0
a = 12; b = -175; c = -1500;
Δ = b2-4ac
Δ = -1752-4·12·(-1500)
Δ = 102625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102625}=\sqrt{25*4105}=\sqrt{25}*\sqrt{4105}=5\sqrt{4105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-5\sqrt{4105}}{2*12}=\frac{175-5\sqrt{4105}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+5\sqrt{4105}}{2*12}=\frac{175+5\sqrt{4105}}{24} $
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