(3x-11)(8x-14)=0

Solution for (3x-11)(8x-14)=0 equation:

(3x-11)(8x-14)=0

We multiply parentheses ..

(+24x^2-42x-88x+154)=0

We get rid of parentheses

24x^2-42x-88x+154=0

We add all the numbers together, and all the variables

24x^2-130x+154=0

a = 24; b = -130; c = +154;
Δ = b2-4ac
Δ = -1302-4·24·154
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-46}{2*24}=\frac{84}{48}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+46}{2*24}=\frac{176}{48}
=3+2/3
$