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7x^2=77
We move all terms to the left:
7x^2-(77)=0
a = 7; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·7·(-77)
Δ = 2156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2156}=\sqrt{196*11}=\sqrt{196}*\sqrt{11}=14\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{11}}{2*7}=\frac{0-14\sqrt{11}}{14} =-\frac{14\sqrt{11}}{14} =-\sqrt{11} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{11}}{2*7}=\frac{0+14\sqrt{11}}{14} =\frac{14\sqrt{11}}{14} =\sqrt{11} $
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