14x=x2+36

Solution for 14x=x2+36 equation:

14x=x2+36

We move all terms to the left:

14x-(x2+36)=0

We add all the numbers together, and all the variables

-(+x^2+36)+14x=0

We get rid of parentheses

-x^2+14x-36=0

We add all the numbers together, and all the variables

-1x^2+14x-36=0

a = -1; b = 14; c = -36;
Δ = b2-4ac
Δ = 142-4·(-1)·(-36)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{13}}{2*-1}=\frac{-14-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{13}}{2*-1}=\frac{-14+2\sqrt{13}}{-2}
$