8x(x+2)=42

Solution for 8x(x+2)=42 equation:

8x(x+2)=42

We move all terms to the left:

8x(x+2)-(42)=0

We multiply parentheses

8x^2+16x-42=0

a = 8; b = 16; c = -42;
Δ = b2-4ac
Δ = 162-4·8·(-42)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*8}=\frac{24}{16}
=1+1/2
$