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(3x+4)-(4x-7)/5x+9=2/3
We move all terms to the left:
(3x+4)-(4x-7)/5x+9-(2/3)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
(3x+4)-(4x-7)/5x+9-(+2/3)=0
We get rid of parentheses
3x-(4x-7)/5x+4+9-2/3=0
We calculate fractions
3x+(-12x+21)/15x+(-10x)/15x+4+9=0
We add all the numbers together, and all the variables
3x+(-12x+21)/15x+(-10x)/15x+13=0
We multiply all the terms by the denominator
3x*15x+(-12x+21)+(-10x)+13*15x=0
Wy multiply elements
45x^2+(-12x+21)+(-10x)+195x=0
We get rid of parentheses
45x^2-12x-10x+195x+21=0
We add all the numbers together, and all the variables
45x^2+173x+21=0
a = 45; b = 173; c = +21;
Δ = b2-4ac
Δ = 1732-4·45·21
Δ = 26149
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{-(173)-\sqrt{26149}}{2*45}=\frac{-173-\sqrt{26149}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(173)+\sqrt{26149}}{2*45}=\frac{-173+\sqrt{26149}}{90} $
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