2x(3x+8)=10

Solution for 2x(3x+8)=10 equation:

2x(3x+8)=10

We move all terms to the left:

2x(3x+8)-(10)=0

We multiply parentheses

6x^2+16x-10=0

a = 6; b = 16; c = -10;
Δ = b2-4ac
Δ = 162-4·6·(-10)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{31}}{2*6}=\frac{-16-4\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{31}}{2*6}=\frac{-16+4\sqrt{31}}{12}
$