0.4x-2.5=1/3x+4.7

Solution for 0.4x-2.5=1/3x+4.7 equation:

0.4x-2.5=1/3x+4.7

We move all terms to the left:

0.4x-2.5-(1/3x+4.7)=0


Domain of the equation: 3x+4.7)!=0

x∈R


We get rid of parentheses

0.4x-1/3x-4.7-2.5=0

We multiply all the terms by the denominator


(0.4x)*3x-(4.7)*3x-(2.5)*3x-1=0

We add all the numbers together, and all the variables

(+0.4x)*3x-(4.7)*3x-(2.5)*3x-1=0

We multiply parentheses

0x^2-14.1x-7.5x-1=0

We add all the numbers together, and all the variables

x^2-21.6x-1=0

a = 1; b = -21.6; c = -1;
Δ = b2-4ac
Δ = -21.62-4·1·(-1)
Δ = 470.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21.6)-\sqrt{470.56}}{2*1}=\frac{21.6-\sqrt{470.56}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21.6)+\sqrt{470.56}}{2*1}=\frac{21.6+\sqrt{470.56}}{2}
$