10x-6/2x+10=1

Solution for 10x-6/2x+10=1 equation:

10x-6/2x+10=1

We move all terms to the left:

10x-6/2x+10-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

10x-6/2x+9=0

We multiply all the terms by the denominator


10x*2x+9*2x-6=0

Wy multiply elements

20x^2+18x-6=0

a = 20; b = 18; c = -6;
Δ = b2-4ac
Δ = 182-4·20·(-6)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{201}}{2*20}=\frac{-18-2\sqrt{201}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{201}}{2*20}=\frac{-18+2\sqrt{201}}{40}
$