14x-x^2=15

Solution for 14x-x^2=15 equation:

14x-x^2=15

We move all terms to the left:

14x-x^2-(15)=0

We add all the numbers together, and all the variables

-1x^2+14x-15=0

a = -1; b = 14; c = -15;
Δ = b2-4ac
Δ = 142-4·(-1)·(-15)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{34}}{2*-1}=\frac{-14-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{34}}{2*-1}=\frac{-14+2\sqrt{34}}{-2}
$