2/3x+15=6x-13

Solution for 2/3x+15=6x-13 equation:

2/3x+15=6x-13

We move all terms to the left:

2/3x+15-(6x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-6x+13+15=0

We multiply all the terms by the denominator


-6x*3x+13*3x+15*3x+2=0

Wy multiply elements

-18x^2+39x+45x+2=0

We add all the numbers together, and all the variables

-18x^2+84x+2=0

a = -18; b = 84; c = +2;
Δ = b2-4ac
Δ = 842-4·(-18)·2
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-60\sqrt{2}}{2*-18}=\frac{-84-60\sqrt{2}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+60\sqrt{2}}{2*-18}=\frac{-84+60\sqrt{2}}{-36}
$