(x-1)2+11x+199=3x2-(x-2)2

Solution for (x-1)2+11x+199=3x2-(x-2)2 equation:

(x-1)2+11x+199=3x^2-(x-2)2

We move all terms to the left:

(x-1)2+11x+199-(3x^2-(x-2)2)=0

We add all the numbers together, and all the variables

11x+(x-1)2-(3x^2-(x-2)2)+199=0

We multiply parentheses

11x+2x-(3x^2-(x-2)2)-2+199=0


We calculate terms in parentheses: -(3x^2-(x-2)2), so:

3x^2-(x-2)2

We multiply parentheses

3x^2-2x+4

Back to the equation:

-(3x^2-2x+4)


We add all the numbers together, and all the variables

13x-(3x^2-2x+4)+197=0

We get rid of parentheses

-3x^2+13x+2x-4+197=0

We add all the numbers together, and all the variables

-3x^2+15x+193=0

a = -3; b = 15; c = +193;
Δ = b2-4ac
Δ = 152-4·(-3)·193
Δ = 2541
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:

$\sqrt{\Delta}=\sqrt{2541}=\sqrt{121*21}=\sqrt{121}*\sqrt{21}=11\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-11\sqrt{21}}{2*-3}=\frac{-15-11\sqrt{21}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+11\sqrt{21}}{2*-3}=\frac{-15+11\sqrt{21}}{-6}
$