2x(4x+3)+3(2x-1)=31

Solution for 2x(4x+3)+3(2x-1)=31 equation:

2x(4x+3)+3(2x-1)=31

We move all terms to the left:

2x(4x+3)+3(2x-1)-(31)=0

We multiply parentheses

8x^2+6x+6x-3-31=0

We add all the numbers together, and all the variables

8x^2+12x-34=0

a = 8; b = 12; c = -34;
Δ = b2-4ac
Δ = 122-4·8·(-34)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{77}}{2*8}=\frac{-12-4\sqrt{77}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{77}}{2*8}=\frac{-12+4\sqrt{77}}{16}
$