89=3x(2x-1)

Solution for 89=3x(2x-1) equation:

89=3x(2x-1)

We move all terms to the left:

89-(3x(2x-1))=0


We calculate terms in parentheses: -(3x(2x-1)), so:

3x(2x-1)

We multiply parentheses

6x^2-3x

Back to the equation:

-(6x^2-3x)


We get rid of parentheses

-6x^2+3x+89=0

a = -6; b = 3; c = +89;
Δ = b2-4ac
Δ = 32-4·(-6)·89
Δ = 2145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{2145}}{2*-6}=\frac{-3-\sqrt{2145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{2145}}{2*-6}=\frac{-3+\sqrt{2145}}{-12}
$