40=3x(5x-10)

Solution for 40=3x(5x-10) equation:

40=3x(5x-10)

We move all terms to the left:

40-(3x(5x-10))=0


We calculate terms in parentheses: -(3x(5x-10)), so:

3x(5x-10)

We multiply parentheses

15x^2-30x

Back to the equation:

-(15x^2-30x)


We get rid of parentheses

-15x^2+30x+40=0

a = -15; b = 30; c = +40;
Δ = b2-4ac
Δ = 302-4·(-15)·40
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{33}}{2*-15}=\frac{-30-10\sqrt{33}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{33}}{2*-15}=\frac{-30+10\sqrt{33}}{-30}
$