-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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1x^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 = 16860
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:

$\sqrt{\Delta}=\sqrt{16860}=\sqrt{4*4215}=\sqrt{4}*\sqrt{4215}=2\sqrt{4215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4215}}{2*-10}=\frac{130-2\sqrt{4215}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4215}}{2*-10}=\frac{130+2\sqrt{4215}}{-20}
$