(4x+1)(7x-9)=x

Solution for (4x+1)(7x-9)=x equation:

(4x+1)(7x-9)=x

We move all terms to the left:

(4x+1)(7x-9)-(x)=0

We add all the numbers together, and all the variables

-1x+(4x+1)(7x-9)=0

We multiply parentheses ..

(+28x^2-36x+7x-9)-1x=0

We get rid of parentheses

28x^2-36x+7x-1x-9=0

We add all the numbers together, and all the variables

28x^2-30x-9=0

a = 28; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·28·(-9)
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{53}}{2*28}=\frac{30-6\sqrt{53}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{53}}{2*28}=\frac{30+6\sqrt{53}}{56}
$