-18.9(3.4x+9)=20/9x+2.5

Solution for -18.9(3.4x+9)=20/9x+2.5 equation:

-18.9(3.4x+9)=20/9x+2.5

We move all terms to the left:

-18.9(3.4x+9)-(20/9x+2.5)=0


Domain of the equation: 9x+2.5)!=0

x∈R


We multiply parentheses

-56.7x-(20/9x+2.5)-170.1=0

We get rid of parentheses

-56.7x-20/9x-2.5-170.1=0

We multiply all the terms by the denominator


-(56.7x)*9x-(2.5)*9x-(170.1)*9x-20=0

We add all the numbers together, and all the variables

-(+56.7x)*9x-(2.5)*9x-(170.1)*9x-20=0

We multiply parentheses

-504x^2-22.5x-1530.9x-20=0

We add all the numbers together, and all the variables

-504x^2-1553.4x-20=0

a = -504; b = -1553.4; c = -20;
Δ = b2-4ac
Δ = -1553.42-4·(-504)·(-20)
Δ = 2372731.56
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{-(-1553.4)-\sqrt{2372731.56}}{2*-504}=\frac{1553.4-\sqrt{2372731.56}}{-1008}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1553.4)+\sqrt{2372731.56}}{2*-504}=\frac{1553.4+\sqrt{2372731.56}}{-1008}
$