110x*x+30*x/2+80*0,25x=26100

Solution for 110x*x+30*x/2+80*0,25x=26100 equation:

110x*x+30x/2+80*0.25x=26100

We move all terms to the left:

110x*x+30x/2+80*0.25x-(26100)=0

Wy multiply elements

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

110x^2*2+30x+0x*2-52200=0

Wy multiply elements

220x^2+30x+0x-52200=0

We add all the numbers together, and all the variables

220x^2+31x-52200=0

a = 220; b = 31; c = -52200;
Δ = b2-4ac
Δ = 312-4·220·(-52200)
Δ = 45936961
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:

$\sqrt{\Delta}=\sqrt{45936961}=\sqrt{49*937489}=\sqrt{49}*\sqrt{937489}=7\sqrt{937489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-7\sqrt{937489}}{2*220}=\frac{-31-7\sqrt{937489}}{440}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+7\sqrt{937489}}{2*220}=\frac{-31+7\sqrt{937489}}{440}
$