3/4x-4=20-2x

Solution for 3/4x-4=20-2x equation:

3/4x-4=20-2x

We move all terms to the left:

3/4x-4-(20-2x)=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+20)-4=0

We get rid of parentheses

3/4x+2x-20-4=0

We multiply all the terms by the denominator


2x*4x-20*4x-4*4x+3=0

Wy multiply elements

8x^2-80x-16x+3=0

We add all the numbers together, and all the variables

8x^2-96x+3=0

a = 8; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·8·3
Δ = 9120
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:

$\sqrt{\Delta}=\sqrt{9120}=\sqrt{16*570}=\sqrt{16}*\sqrt{570}=4\sqrt{570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{570}}{2*8}=\frac{96-4\sqrt{570}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{570}}{2*8}=\frac{96+4\sqrt{570}}{16}
$