(35-2x)(23-2x)=693

Solution for (35-2x)(23-2x)=693 equation:

(35-2x)(23-2x)=693

We move all terms to the left:

(35-2x)(23-2x)-(693)=0

We add all the numbers together, and all the variables

(-2x+35)(-2x+23)-693=0

We multiply parentheses ..

(+4x^2-46x-70x+805)-693=0

We get rid of parentheses

4x^2-46x-70x+805-693=0

We add all the numbers together, and all the variables

4x^2-116x+112=0

a = 4; b = -116; c = +112;
Δ = b2-4ac
Δ = -1162-4·4·112
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-108}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+108}{2*4}=\frac{224}{8}
=28
$