15x-20=x^2

Solution for 15x-20=x^2 equation:

15x-20=x^2

We move all terms to the left:

15x-20-(x^2)=0

determiningTheFunctionDomain
-x^2+15x-20=0

We add all the numbers together, and all the variables

-1x^2+15x-20=0

a = -1; b = 15; c = -20;
Δ = b2-4ac
Δ = 152-4·(-1)·(-20)
Δ = 145
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{145}}{2*-1}=\frac{-15-\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{145}}{2*-1}=\frac{-15+\sqrt{145}}{-2}
$