4x2=3x(-9x+6)

Solution for 4x2=3x(-9x+6) equation:

4x^2=3x(-9x+6)

We move all terms to the left:

4x^2-(3x(-9x+6))=0


We calculate terms in parentheses: -(3x(-9x+6)), so:

3x(-9x+6)

We multiply parentheses

-27x^2+18x

Back to the equation:

-(-27x^2+18x)


We get rid of parentheses

4x^2+27x^2-18x=0

We add all the numbers together, and all the variables

31x^2-18x=0

a = 31; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·31·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*31}=\frac{0}{62}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*31}=\frac{36}{62}
=18/31
$