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7/(4x-3)=2/x+2
We move all terms to the left:
7/(4x-3)-(2/x+2)=0
Domain of the equation: (4x-3)!=0
We move all terms containing x to the left, all other terms to the right
4x!=3
x!=3/4
x!=3/4
x∈R
Domain of the equation: x+2)!=0We get rid of parentheses
x∈R
7/(4x-3)-2/x-2=0
We calculate fractions
7x/(4x^2-3x)+(-8x+6)/(4x^2-3x)-2=0
We multiply all the terms by the denominator
7x+(-8x+6)-2*(4x^2-3x)=0
We multiply parentheses
-8x^2+7x+(-8x+6)+6x=0
We get rid of parentheses
-8x^2+7x-8x+6x+6=0
We add all the numbers together, and all the variables
-8x^2+5x+6=0
a = -8; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-8)·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{-(5)-\sqrt{217}}{2*-8}=\frac{-5-\sqrt{217}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{217}}{2*-8}=\frac{-5+\sqrt{217}}{-16} $
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