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12x^2-190x+527=0
a = 12; b = -190; c = +527;
Δ = b2-4ac
Δ = -1902-4·12·527
Δ = 10804
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10804}=\sqrt{4*2701}=\sqrt{4}*\sqrt{2701}=2\sqrt{2701}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{2701}}{2*12}=\frac{190-2\sqrt{2701}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{2701}}{2*12}=\frac{190+2\sqrt{2701}}{24} $
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