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12x^2-320x-1500=0
a = 12; b = -320; c = -1500;
Δ = b2-4ac
Δ = -3202-4·12·(-1500)
Δ = 174400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{174400}=\sqrt{1600*109}=\sqrt{1600}*\sqrt{109}=40\sqrt{109}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-40\sqrt{109}}{2*12}=\frac{320-40\sqrt{109}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+40\sqrt{109}}{2*12}=\frac{320+40\sqrt{109}}{24} $
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