3x(x-6)=25

Solution for 3x(x-6)=25 equation:

3x(x-6)=25

We move all terms to the left:

3x(x-6)-(25)=0

We multiply parentheses

3x^2-18x-25=0

a = 3; b = -18; c = -25;
Δ = b2-4ac
Δ = -182-4·3·(-25)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{39}}{2*3}=\frac{18-4\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{39}}{2*3}=\frac{18+4\sqrt{39}}{6}
$