6(x-7)x=4

Solution for 6(x-7)x=4 equation:

6(x-7)x=4

We move all terms to the left:

6(x-7)x-(4)=0

We multiply parentheses

6x^2-42x-4=0

a = 6; b = -42; c = -4;
Δ = b2-4ac
Δ = -422-4·6·(-4)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{465}}{2*6}=\frac{42-2\sqrt{465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{465}}{2*6}=\frac{42+2\sqrt{465}}{12}
$