3/4x-1=2x-9

Solution for 3/4x-1=2x-9 equation:

3/4x-1=2x-9

We move all terms to the left:

3/4x-1-(2x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x+9-1=0

We multiply all the terms by the denominator


-2x*4x+9*4x-1*4x+3=0

Wy multiply elements

-8x^2+36x-4x+3=0

We add all the numbers together, and all the variables

-8x^2+32x+3=0

a = -8; b = 32; c = +3;
Δ = b2-4ac
Δ = 322-4·(-8)·3
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{70}}{2*-8}=\frac{-32-4\sqrt{70}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{70}}{2*-8}=\frac{-32+4\sqrt{70}}{-16}
$