-4(3-x)(3-5x)=2(x-3x-1)

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

-4(3-x)(3-5x)=2(x-3x-1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-4(+5x^2-3x-15x+9)-(2(-2x-1))=0


We calculate terms in parentheses: -(2(-2x-1)), so:

2(-2x-1)

We multiply parentheses

-4x-2

Back to the equation:

-(-4x-2)


We multiply parentheses

-20x^2+12x+60x-(-4x-2)-36=0

We get rid of parentheses

-20x^2+12x+60x+4x+2-36=0

We add all the numbers together, and all the variables

-20x^2+76x-34=0

a = -20; b = 76; c = -34;
Δ = b2-4ac
Δ = 762-4·(-20)·(-34)
Δ = 3056
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:

$\sqrt{\Delta}=\sqrt{3056}=\sqrt{16*191}=\sqrt{16}*\sqrt{191}=4\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{191}}{2*-20}=\frac{-76-4\sqrt{191}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{191}}{2*-20}=\frac{-76+4\sqrt{191}}{-40}
$