x+-8/12x-4=-9

Solution for x+-8/12x-4=-9 equation:

x+-8/12x-4=-9

We move all terms to the left:

x+-8/12x-4-(-9)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

x-8/12x+5=0

We multiply all the terms by the denominator


x*12x+5*12x-8=0

Wy multiply elements

12x^2+60x-8=0

a = 12; b = 60; c = -8;
Δ = b2-4ac
Δ = 602-4·12·(-8)
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{249}}{2*12}=\frac{-60-4\sqrt{249}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{249}}{2*12}=\frac{-60+4\sqrt{249}}{24}
$