-4/5x+12=32x=

Solution for -4/5x+12=32x= equation:

-4/5x+12=32x=

We move all terms to the left:

-4/5x+12-(32x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-32x-4/5x+12=0

We multiply all the terms by the denominator


-32x*5x+12*5x-4=0

Wy multiply elements

-160x^2+60x-4=0

a = -160; b = 60; c = -4;
Δ = b2-4ac
Δ = 602-4·(-160)·(-4)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{65}}{2*-160}=\frac{-60-4\sqrt{65}}{-320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{65}}{2*-160}=\frac{-60+4\sqrt{65}}{-320}
$