11x+8=x(2x+5)

Solution for 11x+8=x(2x+5) equation:

11x+8=x(2x+5)

We move all terms to the left:

11x+8-(x(2x+5))=0


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

x(2x+5)

We multiply parentheses

2x^2+5x

Back to the equation:

-(2x^2+5x)


We get rid of parentheses

-2x^2+11x-5x+8=0

We add all the numbers together, and all the variables

-2x^2+6x+8=0

a = -2; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-2)·8
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{-(6)-10}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-2}=\frac{4}{-4}
=-1
$