11x+3=8x(x+4)

Solution for 11x+3=8x(x+4) equation:

11x+3=8x(x+4)

We move all terms to the left:

11x+3-(8x(x+4))=0


We calculate terms in parentheses: -(8x(x+4)), so:

8x(x+4)

We multiply parentheses

8x^2+32x

Back to the equation:

-(8x^2+32x)


We get rid of parentheses

-8x^2+11x-32x+3=0

We add all the numbers together, and all the variables

-8x^2-21x+3=0

a = -8; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·(-8)·3
Δ = 537
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{-(-21)-\sqrt{537}}{2*-8}=\frac{21-\sqrt{537}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{537}}{2*-8}=\frac{21+\sqrt{537}}{-16}
$