3/5x+6(x-2)=0

Solution for 3/5x+6(x-2)=0 equation:

3/5x+6(x-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

3/5x+6x-12=0

We multiply all the terms by the denominator


6x*5x-12*5x+3=0

Wy multiply elements

30x^2-60x+3=0

a = 30; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·30·3
Δ = 3240
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:

$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-18\sqrt{10}}{2*30}=\frac{60-18\sqrt{10}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+18\sqrt{10}}{2*30}=\frac{60+18\sqrt{10}}{60}
$