-6/5x-3/32x+1/5x=-52

Solution for -6/5x-3/32x+1/5x=-52 equation:

-6/5x-3/32x+1/5x=-52

We move all terms to the left:

-6/5x-3/32x+1/5x-(-52)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We add all the numbers together, and all the variables

-6/5x-3/32x+1/5x+52=0

We calculate fractions


(32x-6)/160x^2+(-15x)/160x^2+52=0

We multiply all the terms by the denominator


(32x-6)+(-15x)+52*160x^2=0

Wy multiply elements

8320x^2+(32x-6)+(-15x)=0

We get rid of parentheses

8320x^2+32x-15x-6=0

We add all the numbers together, and all the variables

8320x^2+17x-6=0

a = 8320; b = 17; c = -6;
Δ = b2-4ac
Δ = 172-4·8320·(-6)
Δ = 199969
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:

$\sqrt{\Delta}=\sqrt{199969}=\sqrt{49*4081}=\sqrt{49}*\sqrt{4081}=7\sqrt{4081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7\sqrt{4081}}{2*8320}=\frac{-17-7\sqrt{4081}}{16640}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7\sqrt{4081}}{2*8320}=\frac{-17+7\sqrt{4081}}{16640}
$