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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-(4x+5)-(-1)!=0

x∈R


We multiply all the terms by the denominator


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


We calculate terms in parentheses: -(2x-3(-(-1), so:

2x-3(-(-1

We add all the numbers together, and all the variables

2x

Back to the equation:

-(2x)


We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-2x-(4x+5)=0

We get rid of parentheses

6x^2-2x-4x-5=0

We add all the numbers together, and all the variables

6x^2-6x-5=0

a = 6; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·6·(-5)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*6}=\frac{6-2\sqrt{39}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*6}=\frac{6+2\sqrt{39}}{12}
$