x^2-13x=1/10

Solution for x^2-13x=1/10 equation:

x^2-13x=1/10

We move all terms to the left:

x^2-13x-(1/10)=0

We add all the numbers together, and all the variables

x^2-13x-(+1/10)=0

We get rid of parentheses

x^2-13x-1/10=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-130x-1=0

a = 10; b = -130; c = -1;
Δ = b2-4ac
Δ = -1302-4·10·(-1)
Δ = 16940
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:

$\sqrt{\Delta}=\sqrt{16940}=\sqrt{484*35}=\sqrt{484}*\sqrt{35}=22\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-22\sqrt{35}}{2*10}=\frac{130-22\sqrt{35}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+22\sqrt{35}}{2*10}=\frac{130+22\sqrt{35}}{20}
$