7x^+3x/5x+9=12

Solution for 7x^+3x/5x+9=12 equation:

7x^+3x/5x+9=12

We move all terms to the left:

7x^+3x/5x+9-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7x+3x/5x-3=0

We multiply all the terms by the denominator


7x*5x+3x-3*5x=0

We add all the numbers together, and all the variables

3x+7x*5x-3*5x=0

Wy multiply elements

35x^2+3x-15x=0

We add all the numbers together, and all the variables

35x^2-12x=0

a = 35; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·35·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*35}=\frac{24}{70}
=12/35
$