(3x+4)-(4x-7)/5x+9=3/2

Solution for (3x+4)-(4x-7)/5x+9=3/2 equation:

(3x+4)-(4x-7)/5x+9=3/2

We move all terms to the left:

(3x+4)-(4x-7)/5x+9-(3/2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

(3x+4)-(4x-7)/5x+9-(+3/2)=0

We get rid of parentheses

3x-(4x-7)/5x+4+9-3/2=0

We calculate fractions


3x+(-8x+14)/10x+(-15x)/10x+4+9=0

We add all the numbers together, and all the variables

3x+(-8x+14)/10x+(-15x)/10x+13=0

We multiply all the terms by the denominator


3x*10x+(-8x+14)+(-15x)+13*10x=0

Wy multiply elements

30x^2+(-8x+14)+(-15x)+130x=0

We get rid of parentheses

30x^2-8x-15x+130x+14=0

We add all the numbers together, and all the variables

30x^2+107x+14=0

a = 30; b = 107; c = +14;
Δ = b2-4ac
Δ = 1072-4·30·14
Δ = 9769
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{-(107)-\sqrt{9769}}{2*30}=\frac{-107-\sqrt{9769}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+\sqrt{9769}}{2*30}=\frac{-107+\sqrt{9769}}{60}
$