3x(2x-5)=21

Solution for 3x(2x-5)=21 equation:

3x(2x-5)=21

We move all terms to the left:

3x(2x-5)-(21)=0

We multiply parentheses

6x^2-15x-21=0

a = 6; b = -15; c = -21;
Δ = b2-4ac
Δ = -152-4·6·(-21)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-27}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+27}{2*6}=\frac{42}{12}
=3+1/2
$