(10^-3+10^-2)/(10^-4+10^-2)=x

Solution for (10^-3+10^-2)/(10^-4+10^-2)=x equation:

(10^-3+10^-2)/(10^-4+10^-2)=x

We move all terms to the left:

(10^-3+10^-2)/(10^-4+10^-2)-(x)=0

We add all the numbers together, and all the variables

-1x+(10^-3+10^-2)/(10^-4+10^-2)=0

We multiply all the terms by the denominator


-1x*(10^-4+10^-2)+(10^-3+10^-2)=0

We add all the numbers together, and all the variables

-1x*(10^-4+10^-2)+0.011=0

We multiply parentheses

-10x^2-10x^2+4x+2x+0.011=0

We add all the numbers together, and all the variables

-20x^2+6x+0.011=0

a = -20; b = 6; c = +0.011;
Δ = b2-4ac
Δ = 62-4·(-20)·0.011
Δ = 36.88
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{-(6)-\sqrt{36.88}}{2*-20}=\frac{-6-\sqrt{36.88}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{36.88}}{2*-20}=\frac{-6+\sqrt{36.88}}{-40}
$