x(3/4)-420=6x

Solution for x(3/4)-420=6x equation:

x(3/4)-420=6x

We move all terms to the left:

x(3/4)-420-(6x)=0

We add all the numbers together, and all the variables

x(+3/4)-6x-420=0

We add all the numbers together, and all the variables

-6x+x(+3/4)-420=0

We multiply parentheses

3x^2-6x-420=0

a = 3; b = -6; c = -420;
Δ = b2-4ac
Δ = -62-4·3·(-420)
Δ = 5076
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:

$\sqrt{\Delta}=\sqrt{5076}=\sqrt{36*141}=\sqrt{36}*\sqrt{141}=6\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{141}}{2*3}=\frac{6-6\sqrt{141}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{141}}{2*3}=\frac{6+6\sqrt{141}}{6}
$