2x*x+33x+11=89x+1

Solution for 2x*x+33x+11=89x+1 equation:

2x*x+33x+11=89x+1

We move all terms to the left:

2x*x+33x+11-(89x+1)=0

We add all the numbers together, and all the variables

33x+2x*x-(89x+1)+11=0

Wy multiply elements

2x^2+33x-(89x+1)+11=0

We get rid of parentheses

2x^2+33x-89x-1+11=0

We add all the numbers together, and all the variables

2x^2-56x+10=0

a = 2; b = -56; c = +10;
Δ = b2-4ac
Δ = -562-4·2·10
Δ = 3056
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:

$\sqrt{\Delta}=\sqrt{3056}=\sqrt{16*191}=\sqrt{16}*\sqrt{191}=4\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{191}}{2*2}=\frac{56-4\sqrt{191}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{191}}{2*2}=\frac{56+4\sqrt{191}}{4}
$