15x-10/3x-6=0

Solution for 15x-10/3x-6=0 equation:

15x-10/3x-6=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


15x*3x-6*3x-10=0

Wy multiply elements

45x^2-18x-10=0

a = 45; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·45·(-10)
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{59}}{2*45}=\frac{18-6\sqrt{59}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{59}}{2*45}=\frac{18+6\sqrt{59}}{90}
$