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7x^2-44x-22=0
a = 7; b = -44; c = -22;
Δ = b2-4ac
Δ = -442-4·7·(-22)
Δ = 2552
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2552}=\sqrt{4*638}=\sqrt{4}*\sqrt{638}=2\sqrt{638}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{638}}{2*7}=\frac{44-2\sqrt{638}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{638}}{2*7}=\frac{44+2\sqrt{638}}{14} $
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