1.2x(24.75-0.6x/0.4x)=74.75-1.8x

Solution for 1.2x(24.75-0.6x/0.4x)=74.75-1.8x equation:

1.2x(24.75-0.6x/0.4x)=74.75-1.8x

We move all terms to the left:

1.2x(24.75-0.6x/0.4x)-(74.75-1.8x)=0


Domain of the equation: 0.4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1.2x(-0.6x/0.4x+24.75)-(-1.8x+74.75)=0

We multiply parentheses

0x^2+24.75x-(-1.8x+74.75)=0

We get rid of parentheses

0x^2+24.75x+1.8x-74.75=0

We add all the numbers together, and all the variables

x^2+26.55x-74.75=0

a = 1; b = 26.55; c = -74.75;
Δ = b2-4ac
Δ = 26.552-4·1·(-74.75)
Δ = 1003.9025
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{-(26.55)-\sqrt{1003.9025}}{2*1}=\frac{-26.55-\sqrt{1003.9025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26.55)+\sqrt{1003.9025}}{2*1}=\frac{-26.55+\sqrt{1003.9025}}{2}
$