5/4x-6=2x-9

Solution for 5/4x-6=2x-9 equation:

5/4x-6=2x-9

We move all terms to the left:

5/4x-6-(2x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

5/4x-2x+9-6=0

We multiply all the terms by the denominator


-2x*4x+9*4x-6*4x+5=0

Wy multiply elements

-8x^2+36x-24x+5=0

We add all the numbers together, and all the variables

-8x^2+12x+5=0

a = -8; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-8)·5
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*-8}=\frac{-12-4\sqrt{19}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*-8}=\frac{-12+4\sqrt{19}}{-16}
$