5x+4/4x+6=9x+7/4x-3

Solution for 5x+4/4x+6=9x+7/4x-3 equation:

5x+4/4x+6=9x+7/4x-3

We move all terms to the left:

5x+4/4x+6-(9x+7/4x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

5x+4/4x-9x-7/4x+3+6=0

We multiply all the terms by the denominator


5x*4x-9x*4x+3*4x+6*4x+4-7=0

We add all the numbers together, and all the variables

5x*4x-9x*4x+3*4x+6*4x-3=0

Wy multiply elements

20x^2-36x^2+12x+24x-3=0

We add all the numbers together, and all the variables

-16x^2+36x-3=0

a = -16; b = 36; c = -3;
Δ = b2-4ac
Δ = 362-4·(-16)·(-3)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{69}}{2*-16}=\frac{-36-4\sqrt{69}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{69}}{2*-16}=\frac{-36+4\sqrt{69}}{-32}
$