3/4x-2=-x+3

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

3/4x-2=-x+3

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-12x-8x+3=0

We add all the numbers together, and all the variables

4x^2-20x+3=0

a = 4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·4·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{22}}{2*4}=\frac{20-4\sqrt{22}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{22}}{2*4}=\frac{20+4\sqrt{22}}{8}
$