-4.5(9x-20)3x=4.5x-6

Solution for -4.5(9x-20)3x=4.5x-6 equation:

-4.5(9x-20)3x=4.5x-6

We move all terms to the left:

-4.5(9x-20)3x-(4.5x-6)=0

We multiply parentheses

-117x^2+260x-(4.5x-6)=0

We get rid of parentheses

-117x^2+260x-4.5x+6=0

We add all the numbers together, and all the variables

-117x^2+255.5x+6=0

a = -117; b = 255.5; c = +6;
Δ = b2-4ac
Δ = 255.52-4·(-117)·6
Δ = 68088.25
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{-(255.5)-\sqrt{68088.25}}{2*-117}=\frac{-255.5-\sqrt{68088.25}}{-234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(255.5)+\sqrt{68088.25}}{2*-117}=\frac{-255.5+\sqrt{68088.25}}{-234}
$