(2x-11)(7x-9)=0

Solution for (2x-11)(7x-9)=0 equation:

(2x-11)(7x-9)=0

We multiply parentheses ..

(+14x^2-18x-77x+99)=0

We get rid of parentheses

14x^2-18x-77x+99=0

We add all the numbers together, and all the variables

14x^2-95x+99=0

a = 14; b = -95; c = +99;
Δ = b2-4ac
Δ = -952-4·14·99
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-59}{2*14}=\frac{36}{28}
=1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+59}{2*14}=\frac{154}{28}
=5+1/2
$