10x+9/2x-15=1

Solution for 10x+9/2x-15=1 equation:

10x+9/2x-15=1

We move all terms to the left:

10x+9/2x-15-(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+9/2x-16=0

We multiply all the terms by the denominator


10x*2x-16*2x+9=0

Wy multiply elements

20x^2-32x+9=0

a = 20; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·20·9
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{19}}{2*20}=\frac{32-4\sqrt{19}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{19}}{2*20}=\frac{32+4\sqrt{19}}{40}
$