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4x^2+14x-79=0
a = 4; b = 14; c = -79;
Δ = b2-4ac
Δ = 142-4·4·(-79)
Δ = 1460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{365}}{2*4}=\frac{-14-2\sqrt{365}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{365}}{2*4}=\frac{-14+2\sqrt{365}}{8} $
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