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X2-X=6/7
We move all terms to the left:
X2-X-(6/7)=0
We add all the numbers together, and all the variables
X2-X-(+6/7)=0
We add all the numbers together, and all the variables
X^2-1X-(+6/7)=0
We get rid of parentheses
X^2-1X-6/7=0
We multiply all the terms by the denominator
X^2*7-1X*7-6=0
Wy multiply elements
7X^2-7X-6=0
a = 7; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·7·(-6)
Δ = 217
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{217}}{2*7}=\frac{7-\sqrt{217}}{14} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*7}=\frac{7+\sqrt{217}}{14} $
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