3x+10/8x+7=1

Solution for 3x+10/8x+7=1 equation:

3x+10/8x+7=1

We move all terms to the left:

3x+10/8x+7-(1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3x+10/8x+6=0

We multiply all the terms by the denominator


3x*8x+6*8x+10=0

Wy multiply elements

24x^2+48x+10=0

a = 24; b = 48; c = +10;
Δ = b2-4ac
Δ = 482-4·24·10
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{21}}{2*24}=\frac{-48-8\sqrt{21}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{21}}{2*24}=\frac{-48+8\sqrt{21}}{48}
$