2x(4-7x)=-9

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

2x(4-7x)=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-14x^2+8x+9=0

a = -14; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-14)·9
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{142}}{2*-14}=\frac{-8-2\sqrt{142}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{142}}{2*-14}=\frac{-8+2\sqrt{142}}{-28}
$