(x*x)+1=3x+11

Solution for (x*x)+1=3x+11 equation:

(x*x)+1=3x+11

We move all terms to the left:

(x*x)+1-(3x+11)=0

We add all the numbers together, and all the variables

(+x*x)-(3x+11)+1=0

We get rid of parentheses

x*x-3x-11+1=0

We add all the numbers together, and all the variables

-3x+x*x-10=0

Wy multiply elements

x^2-3x-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$