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14x^2+29x-88=0
a = 14; b = 29; c = -88;
Δ = b2-4ac
Δ = 292-4·14·(-88)
Δ = 5769
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5769}=\sqrt{9*641}=\sqrt{9}*\sqrt{641}=3\sqrt{641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-3\sqrt{641}}{2*14}=\frac{-29-3\sqrt{641}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+3\sqrt{641}}{2*14}=\frac{-29+3\sqrt{641}}{28} $
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