(3x-10)(110-x)=90

Solution for (3x-10)(110-x)=90 equation:

(3x-10)(110-x)=90

We move all terms to the left:

(3x-10)(110-x)-(90)=0

We add all the numbers together, and all the variables

(3x-10)(-1x+110)-90=0

We multiply parentheses ..

(-3x^2+330x+10x-1100)-90=0

We get rid of parentheses

-3x^2+330x+10x-1100-90=0

We add all the numbers together, and all the variables

-3x^2+340x-1190=0

a = -3; b = 340; c = -1190;
Δ = b2-4ac
Δ = 3402-4·(-3)·(-1190)
Δ = 101320
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:

$\sqrt{\Delta}=\sqrt{101320}=\sqrt{4*25330}=\sqrt{4}*\sqrt{25330}=2\sqrt{25330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-2\sqrt{25330}}{2*-3}=\frac{-340-2\sqrt{25330}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+2\sqrt{25330}}{2*-3}=\frac{-340+2\sqrt{25330}}{-6}
$