3/4x+4=40+2x

Solution for 3/4x+4=40+2x equation:

3/4x+4=40+2x

We move all terms to the left:

3/4x+4-(40+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+40)+4=0

We get rid of parentheses

3/4x-2x-40+4=0

We multiply all the terms by the denominator


-2x*4x-40*4x+4*4x+3=0

Wy multiply elements

-8x^2-160x+16x+3=0

We add all the numbers together, and all the variables

-8x^2-144x+3=0

a = -8; b = -144; c = +3;
Δ = b2-4ac
Δ = -1442-4·(-8)·3
Δ = 20832
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:

$\sqrt{\Delta}=\sqrt{20832}=\sqrt{16*1302}=\sqrt{16}*\sqrt{1302}=4\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1302}}{2*-8}=\frac{144-4\sqrt{1302}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1302}}{2*-8}=\frac{144+4\sqrt{1302}}{-16}
$