3x(x-25)-16=8x(45-x)

Solution for 3x(x-25)-16=8x(45-x) equation:

3x(x-25)-16=8x(45-x)

We move all terms to the left:

3x(x-25)-16-(8x(45-x))=0

We add all the numbers together, and all the variables

3x(x-25)-(8x(-1x+45))-16=0

We multiply parentheses

3x^2-75x-(8x(-1x+45))-16=0


We calculate terms in parentheses: -(8x(-1x+45)), so:

8x(-1x+45)

We multiply parentheses

-8x^2+360x

Back to the equation:

-(-8x^2+360x)


We get rid of parentheses

3x^2+8x^2-360x-75x-16=0

We add all the numbers together, and all the variables

11x^2-435x-16=0

a = 11; b = -435; c = -16;
Δ = b2-4ac
Δ = -4352-4·11·(-16)
Δ = 189929
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{-(-435)-\sqrt{189929}}{2*11}=\frac{435-\sqrt{189929}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-435)+\sqrt{189929}}{2*11}=\frac{435+\sqrt{189929}}{22}
$