-7/2x-2=-4-7x

Solution for -7/2x-2=-4-7x equation:

-7/2x-2=-4-7x

We move all terms to the left:

-7/2x-2-(-4-7x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-7/2x-(-7x-4)-2=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

14x^2+8x-4x-7=0

We add all the numbers together, and all the variables

14x^2+4x-7=0

a = 14; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·14·(-7)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{102}}{2*14}=\frac{-4-2\sqrt{102}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{102}}{2*14}=\frac{-4+2\sqrt{102}}{28}
$