-7x+7=-2/6x-4

Solution for -7x+7=-2/6x-4 equation:

-7x+7=-2/6x-4

We move all terms to the left:

-7x+7-(-2/6x-4)=0


Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

-7x+2/6x+4+7=0

We multiply all the terms by the denominator


-7x*6x+4*6x+7*6x+2=0

Wy multiply elements

-42x^2+24x+42x+2=0

We add all the numbers together, and all the variables

-42x^2+66x+2=0

a = -42; b = 66; c = +2;
Δ = b2-4ac
Δ = 662-4·(-42)·2
Δ = 4692
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:

$\sqrt{\Delta}=\sqrt{4692}=\sqrt{4*1173}=\sqrt{4}*\sqrt{1173}=2\sqrt{1173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1173}}{2*-42}=\frac{-66-2\sqrt{1173}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1173}}{2*-42}=\frac{-66+2\sqrt{1173}}{-84}
$