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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-50x+63=0

a = 8; b = -50; c = +63;
Δ = b2-4ac
Δ = -502-4·8·63
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-22}{2*8}=\frac{28}{16}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+22}{2*8}=\frac{72}{16}
=4+1/2
$