3x(-7x+18)=4

Solution for 3x(-7x+18)=4 equation:

3x(-7x+18)=4

We move all terms to the left:

3x(-7x+18)-(4)=0

We multiply parentheses

-21x^2+54x-4=0

a = -21; b = 54; c = -4;
Δ = b2-4ac
Δ = 542-4·(-21)·(-4)
Δ = 2580
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:

$\sqrt{\Delta}=\sqrt{2580}=\sqrt{4*645}=\sqrt{4}*\sqrt{645}=2\sqrt{645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{645}}{2*-21}=\frac{-54-2\sqrt{645}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{645}}{2*-21}=\frac{-54+2\sqrt{645}}{-42}
$