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7x^2-38x-28=0
a = 7; b = -38; c = -28;
Δ = b2-4ac
Δ = -382-4·7·(-28)
Δ = 2228
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2228}=\sqrt{4*557}=\sqrt{4}*\sqrt{557}=2\sqrt{557}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{557}}{2*7}=\frac{38-2\sqrt{557}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{557}}{2*7}=\frac{38+2\sqrt{557}}{14} $
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