(4x+11)=(x*x-10)

Solution for (4x+11)=(x*x-10) equation:

(4x+11)=(x*x-10)

We move all terms to the left:

(4x+11)-((x*x-10))=0

We get rid of parentheses

4x-((x*x-10))+11=0


We calculate terms in parentheses: -((x*x-10)), so:

(x*x-10)

We get rid of parentheses

x*x-10

Wy multiply elements

x^2-10

Back to the equation:

-(x^2-10)


We get rid of parentheses

-x^2+4x+10+11=0

We add all the numbers together, and all the variables

-1x^2+4x+21=0

a = -1; b = 4; c = +21;
Δ = b2-4ac
Δ = 42-4·(-1)·21
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*-1}=\frac{6}{-2}
=-3
$