/4x+5=3x+4

Solution for /4x+5=3x+4 equation:

/4x+5=3x+4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-12x^2-16x+20x=0

We add all the numbers together, and all the variables

-12x^2+4x=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$