2/3x=10x-30

Solution for 2/3x=10x-30 equation:

2/3x=10x-30

We move all terms to the left:

2/3x-(10x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-10x+30=0

We multiply all the terms by the denominator


-10x*3x+30*3x+2=0

Wy multiply elements

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

a = -30; b = 90; c = +2;
Δ = b2-4ac
Δ = 902-4·(-30)·2
Δ = 8340
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:

$\sqrt{\Delta}=\sqrt{8340}=\sqrt{4*2085}=\sqrt{4}*\sqrt{2085}=2\sqrt{2085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2085}}{2*-30}=\frac{-90-2\sqrt{2085}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2085}}{2*-30}=\frac{-90+2\sqrt{2085}}{-60}
$