x(8x+16)=10

Solution for x(8x+16)=10 equation:

x(8x+16)=10

We move all terms to the left:

x(8x+16)-(10)=0

We multiply parentheses

8x^2+16x-10=0

a = 8; b = 16; c = -10;
Δ = b2-4ac
Δ = 162-4·8·(-10)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*8}=\frac{-40}{16}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*8}=\frac{8}{16}
=1/2
$