(54-2x)(35-2x)=429

Solution for (54-2x)(35-2x)=429 equation:

(54-2x)(35-2x)=429

We move all terms to the left:

(54-2x)(35-2x)-(429)=0

We add all the numbers together, and all the variables

(-2x+54)(-2x+35)-429=0

We multiply parentheses ..

(+4x^2-70x-108x+1890)-429=0

We get rid of parentheses

4x^2-70x-108x+1890-429=0

We add all the numbers together, and all the variables

4x^2-178x+1461=0

a = 4; b = -178; c = +1461;
Δ = b2-4ac
Δ = -1782-4·4·1461
Δ = 8308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8308}=\sqrt{4*2077}=\sqrt{4}*\sqrt{2077}=2\sqrt{2077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-2\sqrt{2077}}{2*4}=\frac{178-2\sqrt{2077}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+2\sqrt{2077}}{2*4}=\frac{178+2\sqrt{2077}}{8}
$