(3-2x)(2x+9)-3(5x-1)(4-x)=0

Solution for (3-2x)(2x+9)-3(5x-1)(4-x)=0 equation:

(3-2x)(2x+9)-3(5x-1)(4-x)=0

We add all the numbers together, and all the variables

(-2x+3)(2x+9)-3(5x-1)(-1x+4)=0

We multiply parentheses ..

(-4x^2-18x+6x+27)-3(5x-1)(-1x+4)=0

We get rid of parentheses

-4x^2-18x+6x-3(5x-1)(-1x+4)+27=0

We multiply parentheses ..

-4x^2-3(-5x^2+20x+x-4)-18x+6x+27=0

We add all the numbers together, and all the variables

-4x^2-3(-5x^2+20x+x-4)-12x+27=0

We multiply parentheses

-4x^2+15x^2-60x-3x-12x+12+27=0

We add all the numbers together, and all the variables

11x^2-75x+39=0

a = 11; b = -75; c = +39;
Δ = b2-4ac
Δ = -752-4·11·39
Δ = 3909
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{-(-75)-\sqrt{3909}}{2*11}=\frac{75-\sqrt{3909}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{3909}}{2*11}=\frac{75+\sqrt{3909}}{22}
$