3/4x+2=4x-1

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

3/4x+2=4x-1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+4x+8x+3=0

We add all the numbers together, and all the variables

-16x^2+12x+3=0

a = -16; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-16)·3
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*-16}=\frac{-12-4\sqrt{21}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*-16}=\frac{-12+4\sqrt{21}}{-32}
$