11x(2x-3)=5(2x+2)+5

Solution for 11x(2x-3)=5(2x+2)+5 equation:

11x(2x-3)=5(2x+2)+5

We move all terms to the left:

11x(2x-3)-(5(2x+2)+5)=0

We multiply parentheses

22x^2-33x-(5(2x+2)+5)=0


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

5(2x+2)+5

We multiply parentheses

10x+10+5

We add all the numbers together, and all the variables

10x+15

Back to the equation:

-(10x+15)


We get rid of parentheses

22x^2-33x-10x-15=0

We add all the numbers together, and all the variables

22x^2-43x-15=0

a = 22; b = -43; c = -15;
Δ = b2-4ac
Δ = -432-4·22·(-15)
Δ = 3169
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{-(-43)-\sqrt{3169}}{2*22}=\frac{43-\sqrt{3169}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{3169}}{2*22}=\frac{43+\sqrt{3169}}{44}
$