x2+20x+5=6x2

Solution for x2+20x+5=6x2 equation:

x2+20x+5=6x^2

We move all terms to the left:

x2+20x+5-(6x^2)=0

determiningTheFunctionDomain
-6x^2+x2+20x+5=0

We add all the numbers together, and all the variables

-5x^2+20x+5=0

a = -5; b = 20; c = +5;
Δ = b2-4ac
Δ = 202-4·(-5)·5
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{5}}{2*-5}=\frac{-20-10\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{5}}{2*-5}=\frac{-20+10\sqrt{5}}{-10}
$