2x-1=3/4x-19

Solution for 2x-1=3/4x-19 equation:

2x-1=3/4x-19

We move all terms to the left:

2x-1-(3/4x-19)=0


Domain of the equation: 4x-19)!=0

x∈R


We get rid of parentheses

2x-3/4x+19-1=0

We multiply all the terms by the denominator


2x*4x+19*4x-1*4x-3=0

Wy multiply elements

8x^2+76x-4x-3=0

We add all the numbers together, and all the variables

8x^2+72x-3=0

a = 8; b = 72; c = -3;
Δ = b2-4ac
Δ = 722-4·8·(-3)
Δ = 5280
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:

$\sqrt{\Delta}=\sqrt{5280}=\sqrt{16*330}=\sqrt{16}*\sqrt{330}=4\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{330}}{2*8}=\frac{-72-4\sqrt{330}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{330}}{2*8}=\frac{-72+4\sqrt{330}}{16}
$