.4x-8=1/10x+13

Solution for .4x-8=1/10x+13 equation:

.4x-8=1/10x+13

We move all terms to the left:

.4x-8-(1/10x+13)=0


Domain of the equation: 10x+13)!=0

x∈R


We get rid of parentheses

.4x-1/10x-13-8=0

We multiply all the terms by the denominator


(.4x)*10x-13*10x-8*10x-1=0

We add all the numbers together, and all the variables

(+.4x)*10x-13*10x-8*10x-1=0

We multiply parentheses

10x^2-13*10x-8*10x-1=0

Wy multiply elements

10x^2-130x-80x-1=0

We add all the numbers together, and all the variables

10x^2-210x-1=0

a = 10; b = -210; c = -1;
Δ = b2-4ac
Δ = -2102-4·10·(-1)
Δ = 44140
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:

$\sqrt{\Delta}=\sqrt{44140}=\sqrt{4*11035}=\sqrt{4}*\sqrt{11035}=2\sqrt{11035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11035}}{2*10}=\frac{210-2\sqrt{11035}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11035}}{2*10}=\frac{210+2\sqrt{11035}}{20}
$