7x+6/8x+6=57

Solution for 7x+6/8x+6=57 equation:

7x+6/8x+6=57

We move all terms to the left:

7x+6/8x+6-(57)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

7x+6/8x-51=0

We multiply all the terms by the denominator


7x*8x-51*8x+6=0

Wy multiply elements

56x^2-408x+6=0

a = 56; b = -408; c = +6;
Δ = b2-4ac
Δ = -4082-4·56·6
Δ = 165120
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:

$\sqrt{\Delta}=\sqrt{165120}=\sqrt{256*645}=\sqrt{256}*\sqrt{645}=16\sqrt{645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-408)-16\sqrt{645}}{2*56}=\frac{408-16\sqrt{645}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-408)+16\sqrt{645}}{2*56}=\frac{408+16\sqrt{645}}{112}
$