100(2x+5)=784+56x+x^2

Solution for 100(2x+5)=784+56x+x^2 equation:

100(2x+5)=784+56x+x^2

We move all terms to the left:

100(2x+5)-(784+56x+x^2)=0

We multiply parentheses

-(784+56x+x^2)+200x+500=0

We get rid of parentheses

-x^2-56x+200x-784+500=0

We add all the numbers together, and all the variables

-1x^2+144x-284=0

a = -1; b = 144; c = -284;
Δ = b2-4ac
Δ = 1442-4·(-1)·(-284)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-140}{2*-1}=\frac{-284}{-2}
=+142
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+140}{2*-1}=\frac{-4}{-2}
=+2
$