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12x^2-15x-183=0
a = 12; b = -15; c = -183;
Δ = b2-4ac
Δ = -152-4·12·(-183)
Δ = 9009
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9009}=\sqrt{9*1001}=\sqrt{9}*\sqrt{1001}=3\sqrt{1001}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{1001}}{2*12}=\frac{15-3\sqrt{1001}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{1001}}{2*12}=\frac{15+3\sqrt{1001}}{24} $
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