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7x^2=7-7x
We move all terms to the left:
7x^2-(7-7x)=0
We add all the numbers together, and all the variables
7x^2-(-7x+7)=0
We get rid of parentheses
7x^2+7x-7=0
a = 7; b = 7; c = -7;
Δ = b2-4ac
Δ = 72-4·7·(-7)
Δ = 245
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{5}}{2*7}=\frac{-7-7\sqrt{5}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{5}}{2*7}=\frac{-7+7\sqrt{5}}{14} $
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