15x-x^2=49

Solution for 15x-x^2=49 equation:

15x-x^2=49

We move all terms to the left:

15x-x^2-(49)=0

We add all the numbers together, and all the variables

-1x^2+15x-49=0

a = -1; b = 15; c = -49;
Δ = b2-4ac
Δ = 152-4·(-1)·(-49)
Δ = 29
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{-(15)-\sqrt{29}}{2*-1}=\frac{-15-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{29}}{2*-1}=\frac{-15+\sqrt{29}}{-2}
$