3/4x+1=5-2x

Solution for 3/4x+1=5-2x equation:

3/4x+1=5-2x

We move all terms to the left:

3/4x+1-(5-2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-2x+5)+1=0

We get rid of parentheses

3/4x+2x-5+1=0

We multiply all the terms by the denominator


2x*4x-5*4x+1*4x+3=0

Wy multiply elements

8x^2-20x+4x+3=0

We add all the numbers together, and all the variables

8x^2-16x+3=0

a = 8; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·8·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*8}=\frac{16-4\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*8}=\frac{16+4\sqrt{10}}{16}
$