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2x^2+14x-338=0
a = 2; b = 14; c = -338;
Δ = b2-4ac
Δ = 142-4·2·(-338)
Δ = 2900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{29}}{2*2}=\frac{-14-10\sqrt{29}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{29}}{2*2}=\frac{-14+10\sqrt{29}}{4} $
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