3x*(2x-5)=684

Solution for 3x*(2x-5)=684 equation:

3x*(2x-5)=684

We move all terms to the left:

3x*(2x-5)-(684)=0

We multiply parentheses

6x^2-15x-684=0

a = 6; b = -15; c = -684;
Δ = b2-4ac
Δ = -152-4·6·(-684)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-129}{2*6}=\frac{-114}{12}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+129}{2*6}=\frac{144}{12}
=12
$