0.1x+1.4=-1/3X+4

Solution for 0.1x+1.4=-1/3X+4 equation:

0.1x+1.4=-1/3x+4

We move all terms to the left:

0.1x+1.4-(-1/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

0.1x+1/3x-4+1.4=0

We multiply all the terms by the denominator


(0.1x)*3x-4*3x+(1.4)*3x+1=0

We add all the numbers together, and all the variables

(+0.1x)*3x-4*3x+(1.4)*3x+1=0

We multiply parentheses

0x^2-4*3x+4.2x+1=0

Wy multiply elements

0x^2-12x+4.2x+1=0

We add all the numbers together, and all the variables

x^2-7.8x+1=0

a = 1; b = -7.8; c = +1;
Δ = b2-4ac
Δ = -7.82-4·1·1
Δ = 56.84
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{-(-7.8)-\sqrt{56.84}}{2*1}=\frac{7.8-\sqrt{56.84}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.8)+\sqrt{56.84}}{2*1}=\frac{7.8+\sqrt{56.84}}{2}
$