2x(4x+3)=17

Solution for 2x(4x+3)=17 equation:

2x(4x+3)=17

We move all terms to the left:

2x(4x+3)-(17)=0

We multiply parentheses

8x^2+6x-17=0

a = 8; b = 6; c = -17;
Δ = b2-4ac
Δ = 62-4·8·(-17)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{145}}{2*8}=\frac{-6-2\sqrt{145}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{145}}{2*8}=\frac{-6+2\sqrt{145}}{16}
$