x^2-7x+12=20x^2+x+1

Solution for x^2-7x+12=20x^2+x+1 equation:

x^2-7x+12=20x^2+x+1

We move all terms to the left:

x^2-7x+12-(20x^2+x+1)=0

We get rid of parentheses

x^2-20x^2-7x-x-1+12=0

We add all the numbers together, and all the variables

-19x^2-8x+11=0

a = -19; b = -8; c = +11;
Δ = b2-4ac
Δ = -82-4·(-19)·11
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-30}{2*-19}=\frac{-22}{-38}
=11/19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+30}{2*-19}=\frac{38}{-38}
=-1
$