-11x+10x(x+10)=4-5(2x+11)

Solution for -11x+10x(x+10)=4-5(2x+11) equation:

-11x+10x(x+10)=4-5(2x+11)

We move all terms to the left:

-11x+10x(x+10)-(4-5(2x+11))=0

We multiply parentheses

10x^2-11x+100x-(4-5(2x+11))=0


We calculate terms in parentheses: -(4-5(2x+11)), so:

4-5(2x+11)

determiningTheFunctionDomain
-5(2x+11)+4

We multiply parentheses

-10x-55+4

We add all the numbers together, and all the variables

-10x-51

Back to the equation:

-(-10x-51)


We add all the numbers together, and all the variables

10x^2+89x-(-10x-51)=0

We get rid of parentheses

10x^2+89x+10x+51=0

We add all the numbers together, and all the variables

10x^2+99x+51=0

a = 10; b = 99; c = +51;
Δ = b2-4ac
Δ = 992-4·10·51
Δ = 7761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-\sqrt{7761}}{2*10}=\frac{-99-\sqrt{7761}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+\sqrt{7761}}{2*10}=\frac{-99+\sqrt{7761}}{20}
$