3/10x=3x-18

Solution for 3/10x=3x-18 equation:

3/10x=3x-18

We move all terms to the left:

3/10x-(3x-18)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

3/10x-3x+18=0

We multiply all the terms by the denominator


-3x*10x+18*10x+3=0

Wy multiply elements

-30x^2+180x+3=0

a = -30; b = 180; c = +3;
Δ = b2-4ac
Δ = 1802-4·(-30)·3
Δ = 32760
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:

$\sqrt{\Delta}=\sqrt{32760}=\sqrt{36*910}=\sqrt{36}*\sqrt{910}=6\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{910}}{2*-30}=\frac{-180-6\sqrt{910}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{910}}{2*-30}=\frac{-180+6\sqrt{910}}{-60}
$