(x-11)(2x-31)=0

Solution for (x-11)(2x-31)=0 equation:

(x-11)(2x-31)=0

We multiply parentheses ..

(+2x^2-31x-22x+341)=0

We get rid of parentheses

2x^2-31x-22x+341=0

We add all the numbers together, and all the variables

2x^2-53x+341=0

a = 2; b = -53; c = +341;
Δ = b2-4ac
Δ = -532-4·2·341
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-9}{2*2}=\frac{44}{4}
=11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+9}{2*2}=\frac{62}{4}
=15+1/2
$