100-5x=140-5x(+5x)

Solution for 100-5x=140-5x(+5x) equation:

100-5x=140-5x(+5x)

We move all terms to the left:

100-5x-(140-5x(+5x))=0


We calculate terms in parentheses: -(140-5x(+5x)), so:

140-5x(+5x)

determiningTheFunctionDomain
-5x(+5x)+140

We multiply parentheses

-25x^2+140

Back to the equation:

-(-25x^2+140)


We get rid of parentheses

25x^2-5x-140+100=0

We add all the numbers together, and all the variables

25x^2-5x-40=0

a = 25; b = -5; c = -40;
Δ = b2-4ac
Δ = -52-4·25·(-40)
Δ = 4025
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:

$\sqrt{\Delta}=\sqrt{4025}=\sqrt{25*161}=\sqrt{25}*\sqrt{161}=5\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{161}}{2*25}=\frac{5-5\sqrt{161}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{161}}{2*25}=\frac{5+5\sqrt{161}}{50}
$