4x(x+8)=15(x+1)

Solution for 4x(x+8)=15(x+1) equation:

4x(x+8)=15(x+1)

We move all terms to the left:

4x(x+8)-(15(x+1))=0

We multiply parentheses

4x^2+32x-(15(x+1))=0


We calculate terms in parentheses: -(15(x+1)), so:

15(x+1)

We multiply parentheses

15x+15

Back to the equation:

-(15x+15)


We get rid of parentheses

4x^2+32x-15x-15=0

We add all the numbers together, and all the variables

4x^2+17x-15=0

a = 4; b = 17; c = -15;
Δ = b2-4ac
Δ = 172-4·4·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*4}=\frac{6}{8}
=3/4
$