(23-2x)(31-2x)=273

Solution for (23-2x)(31-2x)=273 equation:

(23-2x)(31-2x)=273

We move all terms to the left:

(23-2x)(31-2x)-(273)=0

We add all the numbers together, and all the variables

(-2x+23)(-2x+31)-273=0

We multiply parentheses ..

(+4x^2-62x-46x+713)-273=0

We get rid of parentheses

4x^2-62x-46x+713-273=0

We add all the numbers together, and all the variables

4x^2-108x+440=0

a = 4; b = -108; c = +440;
Δ = b2-4ac
Δ = -1082-4·4·440
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-68}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+68}{2*4}=\frac{176}{8}
=22
$