-4/3x=3x+15

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

-4/3x=3x+15

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-4/3x-3x-15=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-45x-4=0

a = -9; b = -45; c = -4;
Δ = b2-4ac
Δ = -452-4·(-9)·(-4)
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{209}}{2*-9}=\frac{45-3\sqrt{209}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{209}}{2*-9}=\frac{45+3\sqrt{209}}{-18}
$