4(0.2x-6)=4/5x-2.4

Solution for 4(0.2x-6)=4/5x-2.4 equation:

4(0.2x-6)=4/5x-2.4

We move all terms to the left:

4(0.2x-6)-(4/5x-2.4)=0


Domain of the equation: 5x-2.4)!=0

x∈R


We multiply parentheses

0x-(4/5x-2.4)-24=0

We get rid of parentheses

0x-4/5x+2.4-24=0

We multiply all the terms by the denominator


0x*5x+(2.4)*5x-24*5x-4=0

We multiply parentheses

0x*5x+12x-24*5x-4=0

Wy multiply elements

0x^2+12x-120x-4=0

We add all the numbers together, and all the variables

x^2-108x-4=0

a = 1; b = -108; c = -4;
Δ = b2-4ac
Δ = -1082-4·1·(-4)
Δ = 11680
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:

$\sqrt{\Delta}=\sqrt{11680}=\sqrt{16*730}=\sqrt{16}*\sqrt{730}=4\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{730}}{2*1}=\frac{108-4\sqrt{730}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{730}}{2*1}=\frac{108+4\sqrt{730}}{2}
$