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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(3x(x-1)-4x+), so:

3x(x-1)-4x+

We add all the numbers together, and all the variables

-4x+3x(x-1)

We multiply parentheses

3x^2-4x-3x

We add all the numbers together, and all the variables

3x^2-7x

Back to the equation:

-(3x^2-7x)



We calculate terms in parentheses: -(5x-(4x+5)), so:

5x-(4x+5)

We get rid of parentheses

5x-4x-5

We add all the numbers together, and all the variables

x-5

Back to the equation:

-(x-5)


We get rid of parentheses

-3x^2+3x+7x-x+5+1=0

We add all the numbers together, and all the variables

-3x^2+9x+6=0

a = -3; b = 9; c = +6;
Δ = b2-4ac
Δ = 92-4·(-3)·6
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-3}=\frac{-9-3\sqrt{17}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-3}=\frac{-9+3\sqrt{17}}{-6}
$