8x-6/4x+10=1

Solution for 8x-6/4x+10=1 equation:

8x-6/4x+10=1

We move all terms to the left:

8x-6/4x+10-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8x-6/4x+9=0

We multiply all the terms by the denominator


8x*4x+9*4x-6=0

Wy multiply elements

32x^2+36x-6=0

a = 32; b = 36; c = -6;
Δ = b2-4ac
Δ = 362-4·32·(-6)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{129}}{2*32}=\frac{-36-4\sqrt{129}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{129}}{2*32}=\frac{-36+4\sqrt{129}}{64}
$