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

Solution for 15/(x-4)+15(x+4)=4 equation:

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

We move all terms to the left:

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


Domain of the equation: (x-4)!=0

We move all terms containing x to the left, all other terms to the right

x!=4

x∈R


We multiply parentheses

15/(x-4)+15x+60-4=0

We multiply all the terms by the denominator


15x*(x-4)+60*(x-4)-4*(x-4)+15=0

We multiply parentheses

15x^2-60x+60x-4x-240+16+15=0

We add all the numbers together, and all the variables

15x^2-4x-209=0

a = 15; b = -4; c = -209;
Δ = b2-4ac
Δ = -42-4·15·(-209)
Δ = 12556
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:

$\sqrt{\Delta}=\sqrt{12556}=\sqrt{4*3139}=\sqrt{4}*\sqrt{3139}=2\sqrt{3139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{3139}}{2*15}=\frac{4-2\sqrt{3139}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{3139}}{2*15}=\frac{4+2\sqrt{3139}}{30}
$