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

We add all the numbers together, and all the variables

(+2x.)*4x-40*4x-4*4x+3=0

We multiply parentheses

8x^2-40*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^2-176x+3=0

a = 8; b = -176; c = +3;
Δ = b2-4ac
Δ = -1762-4·8·3
Δ = 30880
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:

$\sqrt{\Delta}=\sqrt{30880}=\sqrt{16*1930}=\sqrt{16}*\sqrt{1930}=4\sqrt{1930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1930}}{2*8}=\frac{176-4\sqrt{1930}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1930}}{2*8}=\frac{176+4\sqrt{1930}}{16}
$