146689+766x+x^2=20x^2

Solution for 146689+766x+x^2=20x^2 equation:

146689+766x+x^2=20x^2

We move all terms to the left:

146689+766x+x^2-(20x^2)=0

determiningTheFunctionDomain
x^2-20x^2+766x+146689=0

We add all the numbers together, and all the variables

-19x^2+766x+146689=0

a = -19; b = 766; c = +146689;
Δ = b2-4ac
Δ = 7662-4·(-19)·146689
Δ = 11735120
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:

$\sqrt{\Delta}=\sqrt{11735120}=\sqrt{2347024*5}=\sqrt{2347024}*\sqrt{5}=1532\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(766)-1532\sqrt{5}}{2*-19}=\frac{-766-1532\sqrt{5}}{-38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(766)+1532\sqrt{5}}{2*-19}=\frac{-766+1532\sqrt{5}}{-38}
$