(4x-7)(2x+9)-2x(x+3)=0

Solution for (4x-7)(2x+9)-2x(x+3)=0 equation:

(4x-7)(2x+9)-2x(x+3)=0

We multiply parentheses

-2x^2+(4x-7)(2x+9)-6x=0

We multiply parentheses ..

-2x^2+(+8x^2+36x-14x-63)-6x=0

We get rid of parentheses

-2x^2+8x^2+36x-14x-6x-63=0

We add all the numbers together, and all the variables

6x^2+16x-63=0

a = 6; b = 16; c = -63;
Δ = b2-4ac
Δ = 162-4·6·(-63)
Δ = 1768
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:

$\sqrt{\Delta}=\sqrt{1768}=\sqrt{4*442}=\sqrt{4}*\sqrt{442}=2\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{442}}{2*6}=\frac{-16-2\sqrt{442}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{442}}{2*6}=\frac{-16+2\sqrt{442}}{12}
$