12-4/5x=4x-6.4

Solution for 12-4/5x=4x-6.4 equation:

12-4/5x=4x-6.4

We move all terms to the left:

12-4/5x-(4x-6.4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-4/5x-4x+6.4+12=0

We multiply all the terms by the denominator


-4x*5x+(6.4)*5x+12*5x-4=0

We multiply parentheses

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

Wy multiply elements

-20x^2+32x+60x-4=0

We add all the numbers together, and all the variables

-20x^2+92x-4=0

a = -20; b = 92; c = -4;
Δ = b2-4ac
Δ = 922-4·(-20)·(-4)
Δ = 8144
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:

$\sqrt{\Delta}=\sqrt{8144}=\sqrt{16*509}=\sqrt{16}*\sqrt{509}=4\sqrt{509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{509}}{2*-20}=\frac{-92-4\sqrt{509}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{509}}{2*-20}=\frac{-92+4\sqrt{509}}{-40}
$