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7x^2+78x+11=0
a = 7; b = 78; c = +11;
Δ = b2-4ac
Δ = 782-4·7·11
Δ = 5776
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{5776}=76$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-76}{2*7}=\frac{-154}{14} =-11 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+76}{2*7}=\frac{-2}{14} =-1/7 $
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