(1-5x)(1+5x)=-19

Solution for (1-5x)(1+5x)=-19 equation:

(1-5x)(1+5x)=-19

We move all terms to the left:

(1-5x)(1+5x)-(-19)=0

We add all the numbers together, and all the variables

(-5x+1)(5x+1)-(-19)=0

We add all the numbers together, and all the variables

(-5x+1)(5x+1)+19=0

We multiply parentheses ..

(-25x^2-5x+5x+1)+19=0

We get rid of parentheses

-25x^2-5x+5x+1+19=0

We add all the numbers together, and all the variables

-25x^2+20=0

a = -25; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-25)·20
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*-25}=\frac{0-20\sqrt{5}}{-50}
=-\frac{20\sqrt{5}}{-50}
=-\frac{2\sqrt{5}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*-25}=\frac{0+20\sqrt{5}}{-50}
=\frac{20\sqrt{5}}{-50}
=\frac{2\sqrt{5}}{-5}
$