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12x^2+84x+115=0
a = 12; b = 84; c = +115;
Δ = b2-4ac
Δ = 842-4·12·115
Δ = 1536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-16\sqrt{6}}{2*12}=\frac{-84-16\sqrt{6}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+16\sqrt{6}}{2*12}=\frac{-84+16\sqrt{6}}{24} $
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