3(0.5x-4)=3/4x-1.2

Solution for 3(0.5x-4)=3/4x-1.2 equation:

3(0.5x-4)=3/4x-1.2

We move all terms to the left:

3(0.5x-4)-(3/4x-1.2)=0


Domain of the equation: 4x-1.2)!=0

x∈R


We multiply parentheses

0x-(3/4x-1.2)-12=0

We get rid of parentheses

0x-3/4x+1.2-12=0

We multiply all the terms by the denominator


0x*4x+(1.2)*4x-12*4x-3=0

We multiply parentheses

0x*4x+4.8x-12*4x-3=0

Wy multiply elements

0x^2+4.8x-48x-3=0

We add all the numbers together, and all the variables

x^2-43.2x-3=0

a = 1; b = -43.2; c = -3;
Δ = b2-4ac
Δ = -43.22-4·1·(-3)
Δ = 1878.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43.2)-\sqrt{1878.24}}{2*1}=\frac{43.2-\sqrt{1878.24}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43.2)+\sqrt{1878.24}}{2*1}=\frac{43.2+\sqrt{1878.24}}{2}
$