5/3x+15=2x+10

Solution for 5/3x+15=2x+10 equation:

5/3x+15=2x+10

We move all terms to the left:

5/3x+15-(2x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-2x-10+15=0

We multiply all the terms by the denominator


-2x*3x-10*3x+15*3x+5=0

Wy multiply elements

-6x^2-30x+45x+5=0

We add all the numbers together, and all the variables

-6x^2+15x+5=0

a = -6; b = 15; c = +5;
Δ = b2-4ac
Δ = 152-4·(-6)·5
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{345}}{2*-6}=\frac{-15-\sqrt{345}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{345}}{2*-6}=\frac{-15+\sqrt{345}}{-12}
$