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

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

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


Domain of the equation: x+3)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

2/x-4x+3+4=0

We multiply all the terms by the denominator


-4x*x+3*x+4*x+2=0

We add all the numbers together, and all the variables

7x-4x*x+2=0

Wy multiply elements

-4x^2+7x+2=0

a = -4; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-4)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*-4}=\frac{2}{-8}
=-1/4
$