2/3x+42=2x-30

Solution for 2/3x+42=2x-30 equation:

2/3x+42=2x-30

We move all terms to the left:

2/3x+42-(2x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-2x+30+42=0

We multiply all the terms by the denominator


-2x*3x+30*3x+42*3x+2=0

Wy multiply elements

-6x^2+90x+126x+2=0

We add all the numbers together, and all the variables

-6x^2+216x+2=0

a = -6; b = 216; c = +2;
Δ = b2-4ac
Δ = 2162-4·(-6)·2
Δ = 46704
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:

$\sqrt{\Delta}=\sqrt{46704}=\sqrt{16*2919}=\sqrt{16}*\sqrt{2919}=4\sqrt{2919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-4\sqrt{2919}}{2*-6}=\frac{-216-4\sqrt{2919}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+4\sqrt{2919}}{2*-6}=\frac{-216+4\sqrt{2919}}{-12}
$