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5x^2+78x-81=0
a = 5; b = 78; c = -81;
Δ = b2-4ac
Δ = 782-4·5·(-81)
Δ = 7704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7704}=\sqrt{36*214}=\sqrt{36}*\sqrt{214}=6\sqrt{214}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{214}}{2*5}=\frac{-78-6\sqrt{214}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{214}}{2*5}=\frac{-78+6\sqrt{214}}{10} $
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