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12x^2-160x+375=0
a = 12; b = -160; c = +375;
Δ = b2-4ac
Δ = -1602-4·12·375
Δ = 7600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-20\sqrt{19}}{2*12}=\frac{160-20\sqrt{19}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{19}}{2*12}=\frac{160+20\sqrt{19}}{24} $
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