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

Solution for (54-2x)(35-2x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-178x+1890=0

a = 4; b = -178; c = +1890;
Δ = b2-4ac
Δ = -1782-4·4·1890
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-38}{2*4}=\frac{140}{8}
=17+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+38}{2*4}=\frac{216}{8}
=27
$