3/5x=6x-18

Solution for 3/5x=6x-18 equation:

3/5x=6x-18

We move all terms to the left:

3/5x-(6x-18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-6x+18=0

We multiply all the terms by the denominator


-6x*5x+18*5x+3=0

Wy multiply elements

-30x^2+90x+3=0

a = -30; b = 90; c = +3;
Δ = b2-4ac
Δ = 902-4·(-30)·3
Δ = 8460
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:

$\sqrt{\Delta}=\sqrt{8460}=\sqrt{36*235}=\sqrt{36}*\sqrt{235}=6\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{235}}{2*-30}=\frac{-90-6\sqrt{235}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{235}}{2*-30}=\frac{-90+6\sqrt{235}}{-60}
$