10-3x*10x=1/10

Solution for 10-3x*10x=1/10 equation:

10-3x*10x=1/10

We move all terms to the left:

10-3x*10x-(1/10)=0

We add all the numbers together, and all the variables

-3x*10x+10-(+1/10)=0

Wy multiply elements

-30x^2+10-(+1/10)=0

We get rid of parentheses

-30x^2+10-1/10=0

We multiply all the terms by the denominator


-30x^2*10-1+10*10=0

We add all the numbers together, and all the variables

-30x^2*10+99=0

Wy multiply elements

-300x^2+99=0

a = -300; b = 0; c = +99;
Δ = b2-4ac
Δ = 02-4·(-300)·99
Δ = 118800
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:

$\sqrt{\Delta}=\sqrt{118800}=\sqrt{3600*33}=\sqrt{3600}*\sqrt{33}=60\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{33}}{2*-300}=\frac{0-60\sqrt{33}}{-600}
=-\frac{60\sqrt{33}}{-600}
=-\frac{\sqrt{33}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{33}}{2*-300}=\frac{0+60\sqrt{33}}{-600}
=\frac{60\sqrt{33}}{-600}
=\frac{\sqrt{33}}{-10}
$