3/4x-13=x-9

Solution for 3/4x-13=x-9 equation:

3/4x-13=x-9

We move all terms to the left:

3/4x-13-(x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x+9-13=0

We multiply all the terms by the denominator


-x*4x+9*4x-13*4x+3=0

Wy multiply elements

-4x^2+36x-52x+3=0

We add all the numbers together, and all the variables

-4x^2-16x+3=0

a = -4; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-4)·3
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{-(-16)-4\sqrt{19}}{2*-4}=\frac{16-4\sqrt{19}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*-4}=\frac{16+4\sqrt{19}}{-8}
$