14x(x+1)=x2+3

Solution for 14x(x+1)=x2+3 equation:

14x(x+1)=x2+3

We move all terms to the left:

14x(x+1)-(x2+3)=0

We add all the numbers together, and all the variables

-(+x^2+3)+14x(x+1)=0

We multiply parentheses

-(+x^2+3)+14x^2+14x=0

We get rid of parentheses

-x^2+14x^2+14x-3=0

We add all the numbers together, and all the variables

13x^2+14x-3=0

a = 13; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·13·(-3)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{22}}{2*13}=\frac{-14-4\sqrt{22}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{22}}{2*13}=\frac{-14+4\sqrt{22}}{26}
$