x(x+5)=6x^2+1

Solution for x(x+5)=6x^2+1 equation:

x(x+5)=6x^2+1

We move all terms to the left:

x(x+5)-(6x^2+1)=0

We multiply parentheses

x^2+5x-(6x^2+1)=0

We get rid of parentheses

x^2-6x^2+5x-1=0

We add all the numbers together, and all the variables

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

a = -5; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-5)·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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