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

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

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

We multiply parentheses ..

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

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