5=6x(x-3)

Solution for 5=6x(x-3) equation:

5=6x(x-3)

We move all terms to the left:

5-(6x(x-3))=0


We calculate terms in parentheses: -(6x(x-3)), so:

6x(x-3)

We multiply parentheses

6x^2-18x

Back to the equation:

-(6x^2-18x)


We get rid of parentheses

-6x^2+18x+5=0

a = -6; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-6)·5
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{111}}{2*-6}=\frac{-18-2\sqrt{111}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{111}}{2*-6}=\frac{-18+2\sqrt{111}}{-12}
$