(3x-5)(8x-11)=0

Solution for (3x-5)(8x-11)=0 equation:

(3x-5)(8x-11)=0

We multiply parentheses ..

(+24x^2-33x-40x+55)=0

We get rid of parentheses

24x^2-33x-40x+55=0

We add all the numbers together, and all the variables

24x^2-73x+55=0

a = 24; b = -73; c = +55;
Δ = b2-4ac
Δ = -732-4·24·55
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-7}{2*24}=\frac{66}{48}
=1+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+7}{2*24}=\frac{80}{48}
=1+2/3
$