-45(9x-20)-3x=4/5x-6

Solution for -45(9x-20)-3x=4/5x-6 equation:

-45(9x-20)-3x=4/5x-6

We move all terms to the left:

-45(9x-20)-3x-(4/5x-6)=0


Domain of the equation: 5x-6)!=0

x∈R


We add all the numbers together, and all the variables

-3x-45(9x-20)-(4/5x-6)=0

We multiply parentheses

-3x-405x-(4/5x-6)+900=0

We get rid of parentheses

-3x-405x-4/5x+6+900=0

We multiply all the terms by the denominator


-3x*5x-405x*5x+6*5x+900*5x-4=0

Wy multiply elements

-15x^2-2025x^2+30x+4500x-4=0

We add all the numbers together, and all the variables

-2040x^2+4530x-4=0

a = -2040; b = 4530; c = -4;
Δ = b2-4ac
Δ = 45302-4·(-2040)·(-4)
Δ = 20488260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20488260}=\sqrt{4*5122065}=\sqrt{4}*\sqrt{5122065}=2\sqrt{5122065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4530)-2\sqrt{5122065}}{2*-2040}=\frac{-4530-2\sqrt{5122065}}{-4080}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4530)+2\sqrt{5122065}}{2*-2040}=\frac{-4530+2\sqrt{5122065}}{-4080}
$