x2=20-19x

Solution for x2=20-19x equation:

x2=20-19x

We move all terms to the left:

x2-(20-19x)=0

We add all the numbers together, and all the variables

x2-(-19x+20)=0

We add all the numbers together, and all the variables

x^2-(-19x+20)=0

We get rid of parentheses

x^2+19x-20=0

a = 1; b = 19; c = -20;
Δ = b2-4ac
Δ = 192-4·1·(-20)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*1}=\frac{2}{2}
=1
$