80x-x^2=102+20x

Solution for 80x-x^2=102+20x equation:

80x-x^2=102+20x

We move all terms to the left:

80x-x^2-(102+20x)=0

We add all the numbers together, and all the variables

-x^2+80x-(20x+102)=0

We add all the numbers together, and all the variables

-1x^2+80x-(20x+102)=0

We get rid of parentheses

-1x^2+80x-20x-102=0

We add all the numbers together, and all the variables

-1x^2+60x-102=0

a = -1; b = 60; c = -102;
Δ = b2-4ac
Δ = 602-4·(-1)·(-102)
Δ = 3192
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:

$\sqrt{\Delta}=\sqrt{3192}=\sqrt{4*798}=\sqrt{4}*\sqrt{798}=2\sqrt{798}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{798}}{2*-1}=\frac{-60-2\sqrt{798}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{798}}{2*-1}=\frac{-60+2\sqrt{798}}{-2}
$