4x-9=5/2x-12

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

4x-9=5/2x-12

We move all terms to the left:

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


Domain of the equation: 2x-12)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


4x*2x+12*2x-9*2x-5=0

Wy multiply elements

8x^2+24x-18x-5=0

We add all the numbers together, and all the variables

8x^2+6x-5=0

a = 8; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·8·(-5)
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{-(6)-14}{2*8}=\frac{-20}{16}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*8}=\frac{8}{16}
=1/2
$