x(29-x)+(26-x)=100

Solution for x(29-x)+(26-x)=100 equation:

x(29-x)+(26-x)=100

We move all terms to the left:

x(29-x)+(26-x)-(100)=0

We add all the numbers together, and all the variables

x(-1x+29)+(-1x+26)-100=0

We multiply parentheses

-1x^2+29x+(-1x+26)-100=0

We get rid of parentheses

-1x^2+29x-1x+26-100=0

We add all the numbers together, and all the variables

-1x^2+28x-74=0

a = -1; b = 28; c = -74;
Δ = b2-4ac
Δ = 282-4·(-1)·(-74)
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{122}}{2*-1}=\frac{-28-2\sqrt{122}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{122}}{2*-1}=\frac{-28+2\sqrt{122}}{-2}
$