2.5+x=3x(72-x)

Solution for 2.5+x=3x(72-x) equation:

2.5+x=3x(72-x)

We move all terms to the left:

2.5+x-(3x(72-x))=0

We add all the numbers together, and all the variables

x-(3x(-1x+72))+2.5=0


We calculate terms in parentheses: -(3x(-1x+72)), so:

3x(-1x+72)

We multiply parentheses

-3x^2+216x

Back to the equation:

-(-3x^2+216x)


We get rid of parentheses

3x^2-216x+x+2.5=0

We add all the numbers together, and all the variables

3x^2-215x+2.5=0

a = 3; b = -215; c = +2.5;
Δ = b2-4ac
Δ = -2152-4·3·2.5
Δ = 46195
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{-(-215)-\sqrt{46195}}{2*3}=\frac{215-\sqrt{46195}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-215)+\sqrt{46195}}{2*3}=\frac{215+\sqrt{46195}}{6}
$