4x=10/3x+15

Solution for 4x=10/3x+15 equation:

4x=10/3x+15

We move all terms to the left:

4x-(10/3x+15)=0


Domain of the equation: 3x+15)!=0

x∈R


We get rid of parentheses

4x-10/3x-15=0

We multiply all the terms by the denominator


4x*3x-15*3x-10=0

Wy multiply elements

12x^2-45x-10=0

a = 12; b = -45; c = -10;
Δ = b2-4ac
Δ = -452-4·12·(-10)
Δ = 2505
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{-(-45)-\sqrt{2505}}{2*12}=\frac{45-\sqrt{2505}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2505}}{2*12}=\frac{45+\sqrt{2505}}{24}
$