(3x-5)x=27.5

Solution for (3x-5)x=27.5 equation:

(3x-5)x=27.5

We move all terms to the left:

(3x-5)x-(27.5)=0

We add all the numbers together, and all the variables

(3x-5)x-27.5=0

We multiply parentheses

3x^2-5x-27.5=0

a = 3; b = -5; c = -27.5;
Δ = b2-4ac
Δ = -52-4·3·(-27.5)
Δ = 355
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{-(-5)-\sqrt{355}}{2*3}=\frac{5-\sqrt{355}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{355}}{2*3}=\frac{5+\sqrt{355}}{6}
$