/4x+12=5x+2

Solution for /4x+12=5x+2 equation:

/4x+12=5x+2

We move all terms to the left:

/4x+12-(5x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

/4x-5x-2+12=0

We multiply all the terms by the denominator


-5x*4x-2*4x+12*4x+=0

We add all the numbers together, and all the variables

-5x*4x-2*4x+12*4x=0

Wy multiply elements

-20x^2-8x+48x=0

We add all the numbers together, and all the variables

-20x^2+40x=0

a = -20; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-20)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-20}=\frac{-80}{-40}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-20}=\frac{0}{-40}
=0
$