8+.7x=6+2/10x

Solution for 8+.7x=6+2/10x equation:

8+.7x=6+2/10x

We move all terms to the left:

8+.7x-(6+2/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.7x-(2/10x+6)+8=0

We get rid of parentheses

.7x-2/10x-6+8=0

We multiply all the terms by the denominator


(.7x)*10x-6*10x+8*10x-2=0

We add all the numbers together, and all the variables

(+.7x)*10x-6*10x+8*10x-2=0

We multiply parentheses

10x^2-6*10x+8*10x-2=0

Wy multiply elements

10x^2-60x+80x-2=0

We add all the numbers together, and all the variables

10x^2+20x-2=0

a = 10; b = 20; c = -2;
Δ = b2-4ac
Δ = 202-4·10·(-2)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{30}}{2*10}=\frac{-20-4\sqrt{30}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{30}}{2*10}=\frac{-20+4\sqrt{30}}{20}
$