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

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

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

We multiply parentheses ..

(+4x^2-12x-11x+33)=0

We get rid of parentheses

4x^2-12x-11x+33=0

We add all the numbers together, and all the variables

4x^2-23x+33=0

a = 4; b = -23; c = +33;
Δ = b2-4ac
Δ = -232-4·4·33
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-1}{2*4}=\frac{22}{8}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+1}{2*4}=\frac{24}{8}
=3
$