2/3x+10=3x-18

Solution for 2/3x+10=3x-18 equation:

2/3x+10=3x-18

We move all terms to the left:

2/3x+10-(3x-18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-3x+18+10=0

We multiply all the terms by the denominator


-3x*3x+18*3x+10*3x+2=0

Wy multiply elements

-9x^2+54x+30x+2=0

We add all the numbers together, and all the variables

-9x^2+84x+2=0

a = -9; b = 84; c = +2;
Δ = b2-4ac
Δ = 842-4·(-9)·2
Δ = 7128
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:

$\sqrt{\Delta}=\sqrt{7128}=\sqrt{324*22}=\sqrt{324}*\sqrt{22}=18\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-18\sqrt{22}}{2*-9}=\frac{-84-18\sqrt{22}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+18\sqrt{22}}{2*-9}=\frac{-84+18\sqrt{22}}{-18}
$