x(3x-10)=21

Solution for x(3x-10)=21 equation:

x(3x-10)=21

We move all terms to the left:

x(3x-10)-(21)=0

We multiply parentheses

3x^2-10x-21=0

a = 3; b = -10; c = -21;
Δ = b2-4ac
Δ = -102-4·3·(-21)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{22}}{2*3}=\frac{10-4\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{22}}{2*3}=\frac{10+4\sqrt{22}}{6}
$