3,75x+18+5.3/4x=6,5x+30

Solution for 3,75x+18+5.3/4x=6,5x+30 equation:

3.75x+18+5.3/4x=6.5x+30

We move all terms to the left:

3.75x+18+5.3/4x-(6.5x+30)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3.75x+5.3/4x-6.5x-30+18=0

We multiply all the terms by the denominator


(3.75x)*4x-(6.5x)*4x-30*4x+18*4x+5.3=0

We add all the numbers together, and all the variables

(+3.75x)*4x-(+6.5x)*4x-30*4x+18*4x+5.3=0

We multiply parentheses

12x^2-24x^2-30*4x+18*4x+5.3=0

Wy multiply elements

12x^2-24x^2-120x+72x+5.3=0

We add all the numbers together, and all the variables

-12x^2-48x+5.3=0

a = -12; b = -48; c = +5.3;
Δ = b2-4ac
Δ = -482-4·(-12)·5.3
Δ = 2558.4
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{-(-48)-\sqrt{2558.4}}{2*-12}=\frac{48-\sqrt{2558.4}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+\sqrt{2558.4}}{2*-12}=\frac{48+\sqrt{2558.4}}{-24}
$