4x(x+8)=-(x-2)+24

Solution for 4x(x+8)=-(x-2)+24 equation:

4x(x+8)=-(x-2)+24

We move all terms to the left:

4x(x+8)-(-(x-2)+24)=0

We multiply parentheses

4x^2+32x-(-(x-2)+24)=0


We calculate terms in parentheses: -(-(x-2)+24), so:

-(x-2)+24

We get rid of parentheses

-x+2+24

We add all the numbers together, and all the variables

-1x+26

Back to the equation:

-(-1x+26)


We get rid of parentheses

4x^2+32x+1x-26=0

We add all the numbers together, and all the variables

4x^2+33x-26=0

a = 4; b = 33; c = -26;
Δ = b2-4ac
Δ = 332-4·4·(-26)
Δ = 1505
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{-(33)-\sqrt{1505}}{2*4}=\frac{-33-\sqrt{1505}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1505}}{2*4}=\frac{-33+\sqrt{1505}}{8}
$