3x-6/15x+2=0

Solution for 3x-6/15x+2=0 equation:

3x-6/15x+2=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We multiply all the terms by the denominator


3x*15x+2*15x-6=0

Wy multiply elements

45x^2+30x-6=0

a = 45; b = 30; c = -6;
Δ = b2-4ac
Δ = 302-4·45·(-6)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{55}}{2*45}=\frac{-30-6\sqrt{55}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{55}}{2*45}=\frac{-30+6\sqrt{55}}{90}
$