1.8(x-5)=1/4x+4.4

Solution for 1.8(x-5)=1/4x+4.4 equation:

1.8(x-5)=1/4x+4.4

We move all terms to the left:

1.8(x-5)-(1/4x+4.4)=0


Domain of the equation: 4x+4.4)!=0

x∈R


We multiply parentheses

1.8x-(1/4x+4.4)-9=0

We get rid of parentheses

1.8x-1/4x-4.4-9=0

We multiply all the terms by the denominator


(1.8x)*4x-(4.4)*4x-9*4x-1=0

We add all the numbers together, and all the variables

(+1.8x)*4x-(4.4)*4x-9*4x-1=0

We multiply parentheses

4x^2-17.6x-9*4x-1=0

Wy multiply elements

4x^2-17.6x-36x-1=0

We add all the numbers together, and all the variables

4x^2-53.6x-1=0

a = 4; b = -53.6; c = -1;
Δ = b2-4ac
Δ = -53.62-4·4·(-1)
Δ = 2888.96
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{-(-53.6)-\sqrt{2888.96}}{2*4}=\frac{53.6-\sqrt{2888.96}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53.6)+\sqrt{2888.96}}{2*4}=\frac{53.6+\sqrt{2888.96}}{8}
$