15x-10/3x-6=1

Solution for 15x-10/3x-6=1 equation:

15x-10/3x-6=1

We move all terms to the left:

15x-10/3x-6-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

15x-10/3x-7=0

We multiply all the terms by the denominator


15x*3x-7*3x-10=0

Wy multiply elements

45x^2-21x-10=0

a = 45; b = -21; c = -10;
Δ = b2-4ac
Δ = -212-4·45·(-10)
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{249}}{2*45}=\frac{21-3\sqrt{249}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{249}}{2*45}=\frac{21+3\sqrt{249}}{90}
$