0.7x-0.9/0.3x-0.7=9

Solution for 0.7x-0.9/0.3x-0.7=9 equation:

0.7x-0.9/0.3x-0.7=9

We move all terms to the left:

0.7x-0.9/0.3x-0.7-(9)=0


Domain of the equation: 0.3x!=0

x!=0/0.3

x!=0

x∈R


We add all the numbers together, and all the variables

0.7x-0.9/0.3x-9.7=0

We multiply all the terms by the denominator


(0.7x)*0.3x-(9.7)*0.3x-0.9=0

We add all the numbers together, and all the variables

(+0.7x)*0.3x-(9.7)*0.3x-0.9=0

We multiply parentheses

0x^2-0x-0.9=0

We add all the numbers together, and all the variables

x^2-1x-0.9=0

a = 1; b = -1; c = -0.9;
Δ = b2-4ac
Δ = -12-4·1·(-0.9)
Δ = 4.6
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{-(-1)-\sqrt{4.6}}{2*1}=\frac{1-\sqrt{4.6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{4.6}}{2*1}=\frac{1+\sqrt{4.6}}{2}
$