0.4=10x(2x-3)

Solution for 0.4=10x(2x-3) equation:

0.4=10x(2x-3)

We move all terms to the left:

0.4-(10x(2x-3))=0


We calculate terms in parentheses: -(10x(2x-3)), so:

10x(2x-3)

We multiply parentheses

20x^2-30x

Back to the equation:

-(20x^2-30x)


We get rid of parentheses

-20x^2+30x+0.4=0

a = -20; b = 30; c = +0.4;
Δ = b2-4ac
Δ = 302-4·(-20)·0.4
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{233}}{2*-20}=\frac{-30-2\sqrt{233}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{233}}{2*-20}=\frac{-30+2\sqrt{233}}{-40}
$