3x+1/5x-6=0

Solution for 3x+1/5x-6=0 equation:

3x+1/5x-6=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


3x*5x-6*5x+1=0

Wy multiply elements

15x^2-30x+1=0

a = 15; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·15·1
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{210}}{2*15}=\frac{30-2\sqrt{210}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{210}}{2*15}=\frac{30+2\sqrt{210}}{30}
$