-7/8x-6=-3x-14

Solution for -7/8x-6=-3x-14 equation:

-7/8x-6=-3x-14

We move all terms to the left:

-7/8x-6-(-3x-14)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

-7/8x+3x+14-6=0

We multiply all the terms by the denominator


3x*8x+14*8x-6*8x-7=0

Wy multiply elements

24x^2+112x-48x-7=0

We add all the numbers together, and all the variables

24x^2+64x-7=0

a = 24; b = 64; c = -7;
Δ = b2-4ac
Δ = 642-4·24·(-7)
Δ = 4768
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:

$\sqrt{\Delta}=\sqrt{4768}=\sqrt{16*298}=\sqrt{16}*\sqrt{298}=4\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{298}}{2*24}=\frac{-64-4\sqrt{298}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{298}}{2*24}=\frac{-64+4\sqrt{298}}{48}
$