(4a-3)(-2a+9)=0

Solution for (4a-3)(-2a+9)=0 equation:

(4a-3)(-2a+9)=0

We multiply parentheses ..

(-8a^2+36a+6a-27)=0

We get rid of parentheses

-8a^2+36a+6a-27=0

We add all the numbers together, and all the variables

-8a^2+42a-27=0

a = -8; b = 42; c = -27;
Δ = b2-4ac
Δ = 422-4·(-8)·(-27)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*-8}=\frac{-72}{-16}
=4+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*-8}=\frac{-12}{-16}
=3/4
$