7(4x-8)(2x-9)=0

Solution for 7(4x-8)(2x-9)=0 equation:

7(4x-8)(2x-9)=0

We multiply parentheses ..

7(+8x^2-36x-16x+72)=0

We multiply parentheses

56x^2-252x-112x+504=0

We add all the numbers together, and all the variables

56x^2-364x+504=0

a = 56; b = -364; c = +504;
Δ = b2-4ac
Δ = -3642-4·56·504
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-140}{2*56}=\frac{224}{112}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+140}{2*56}=\frac{504}{112}
=4+1/2
$