3/10x+1,4=x+2

Solution for 3/10x+1,4=x+2 equation:

3/10x+1.4=x+2

We move all terms to the left:

3/10x+1.4-(x+2)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

3/10x-x-2+1.4=0

We multiply all the terms by the denominator


-x*10x-2*10x+(1.4)*10x+3=0

We multiply parentheses

-x*10x-2*10x+14x+3=0

Wy multiply elements

-10x^2-20x+14x+3=0

We add all the numbers together, and all the variables

-10x^2-6x+3=0

a = -10; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-10)·3
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-10}=\frac{6-2\sqrt{39}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-10}=\frac{6+2\sqrt{39}}{-20}
$