5x+12/2x-9=4

Solution for 5x+12/2x-9=4 equation:

5x+12/2x-9=4

We move all terms to the left:

5x+12/2x-9-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x+12/2x-13=0

We multiply all the terms by the denominator


5x*2x-13*2x+12=0

Wy multiply elements

10x^2-26x+12=0

a = 10; b = -26; c = +12;
Δ = b2-4ac
Δ = -262-4·10·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-14}{2*10}=\frac{12}{20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+14}{2*10}=\frac{40}{20}
=2
$