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7x^2+69x-54=0
a = 7; b = 69; c = -54;
Δ = b2-4ac
Δ = 692-4·7·(-54)
Δ = 6273
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6273}=\sqrt{9*697}=\sqrt{9}*\sqrt{697}=3\sqrt{697}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{697}}{2*7}=\frac{-69-3\sqrt{697}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{697}}{2*7}=\frac{-69+3\sqrt{697}}{14} $
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