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X-5/7X=11
We move all terms to the left:
X-5/7X-(11)=0
Domain of the equation: 7X!=0We multiply all the terms by the denominator
X!=0/7
X!=0
X∈R
X*7X-11*7X-5=0
Wy multiply elements
7X^2-77X-5=0
a = 7; b = -77; c = -5;
Δ = b2-4ac
Δ = -772-4·7·(-5)
Δ = 6069
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{6069}=\sqrt{289*21}=\sqrt{289}*\sqrt{21}=17\sqrt{21}X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-17\sqrt{21}}{2*7}=\frac{77-17\sqrt{21}}{14}X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+17\sqrt{21}}{2*7}=\frac{77+17\sqrt{21}}{14}
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