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12x^2+44x-5=0
a = 12; b = 44; c = -5;
Δ = b2-4ac
Δ = 442-4·12·(-5)
Δ = 2176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{34}}{2*12}=\frac{-44-8\sqrt{34}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{34}}{2*12}=\frac{-44+8\sqrt{34}}{24} $
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