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-14x^2-44x-24=0
a = -14; b = -44; c = -24;
Δ = b2-4ac
Δ = -442-4·(-14)·(-24)
Δ = 592
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{37}}{2*-14}=\frac{44-4\sqrt{37}}{-28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{37}}{2*-14}=\frac{44+4\sqrt{37}}{-28} $
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