110x+30(x/2)+80x(/4)=26100

Solution for 110x+30(x/2)+80x(/4)=26100 equation:

110x+30(x/2)+80x(/4)=26100

We move all terms to the left:

110x+30(x/2)+80x(/4)-(26100)=0

We add all the numbers together, and all the variables

110x+30(+x/2)+80x(+/4)-26100=0

We multiply parentheses

80x^2+110x+30x-26100=0

We add all the numbers together, and all the variables

80x^2+140x-26100=0

a = 80; b = 140; c = -26100;
Δ = b2-4ac
Δ = 1402-4·80·(-26100)
Δ = 8371600
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:

$\sqrt{\Delta}=\sqrt{8371600}=\sqrt{400*20929}=\sqrt{400}*\sqrt{20929}=20\sqrt{20929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-20\sqrt{20929}}{2*80}=\frac{-140-20\sqrt{20929}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+20\sqrt{20929}}{2*80}=\frac{-140+20\sqrt{20929}}{160}
$