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

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

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

We move all terms to the left:

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

We multiply parentheses

-3x-36x-(4/5x-6)+80=0

We get rid of parentheses

-3x-36x-4/5x+6+80=0

We multiply all the terms by the denominator


-3x*5x-36x*5x+6*5x+80*5x-4=0

Wy multiply elements

-15x^2-180x^2+30x+400x-4=0

We add all the numbers together, and all the variables

-195x^2+430x-4=0

a = -195; b = 430; c = -4;
Δ = b2-4ac
Δ = 4302-4·(-195)·(-4)
Δ = 181780
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:

$\sqrt{\Delta}=\sqrt{181780}=\sqrt{4*45445}=\sqrt{4}*\sqrt{45445}=2\sqrt{45445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(430)-2\sqrt{45445}}{2*-195}=\frac{-430-2\sqrt{45445}}{-390}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(430)+2\sqrt{45445}}{2*-195}=\frac{-430+2\sqrt{45445}}{-390}
$