(4x-11)(4x-3)=0

Solution for (4x-11)(4x-3)=0 equation:

(4x-11)(4x-3)=0

We multiply parentheses ..

(+16x^2-12x-44x+33)=0

We get rid of parentheses

16x^2-12x-44x+33=0

We add all the numbers together, and all the variables

16x^2-56x+33=0

a = 16; b = -56; c = +33;
Δ = b2-4ac
Δ = -562-4·16·33
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-32}{2*16}=\frac{24}{32}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+32}{2*16}=\frac{88}{32}
=2+3/4
$