3x+100=5x(200-3x)

Solution for 3x+100=5x(200-3x) equation:

3x+100=5x(200-3x)

We move all terms to the left:

3x+100-(5x(200-3x))=0

We add all the numbers together, and all the variables

3x-(5x(-3x+200))+100=0


We calculate terms in parentheses: -(5x(-3x+200)), so:

5x(-3x+200)

We multiply parentheses

-15x^2+1000x

Back to the equation:

-(-15x^2+1000x)


We get rid of parentheses

15x^2-1000x+3x+100=0

We add all the numbers together, and all the variables

15x^2-997x+100=0

a = 15; b = -997; c = +100;
Δ = b2-4ac
Δ = -9972-4·15·100
Δ = 988009
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{-(-997)-\sqrt{988009}}{2*15}=\frac{997-\sqrt{988009}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-997)+\sqrt{988009}}{2*15}=\frac{997+\sqrt{988009}}{30}
$