16x+100=5x^2-32x

Solution for 16x+100=5x^2-32x equation:

16x+100=5x^2-32x

We move all terms to the left:

16x+100-(5x^2-32x)=0

We get rid of parentheses

-5x^2+16x+32x+100=0

We add all the numbers together, and all the variables

-5x^2+48x+100=0

a = -5; b = 48; c = +100;
Δ = b2-4ac
Δ = 482-4·(-5)·100
Δ = 4304
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:

$\sqrt{\Delta}=\sqrt{4304}=\sqrt{16*269}=\sqrt{16}*\sqrt{269}=4\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{269}}{2*-5}=\frac{-48-4\sqrt{269}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{269}}{2*-5}=\frac{-48+4\sqrt{269}}{-10}
$