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

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

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

We multiply parentheses

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

We add all the numbers together, and all the variables

8x^2-22x-63=0

a = 8; b = -22; c = -63;
Δ = b2-4ac
Δ = -222-4·8·(-63)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-50}{2*8}=\frac{-28}{16}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+50}{2*8}=\frac{72}{16}
=4+1/2
$