26x-x^2=160

Solution for 26x-x^2=160 equation:

26x-x^2=160

We move all terms to the left:

26x-x^2-(160)=0

We add all the numbers together, and all the variables

-1x^2+26x-160=0

a = -1; b = 26; c = -160;
Δ = b2-4ac
Δ = 262-4·(-1)·(-160)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6}{2*-1}=\frac{-20}{-2}
=+10
$