2x(4x+3)=3+x

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

2x(4x+3)=3+x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+6x-(x+3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2+5x-3=0

a = 8; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·8·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*8}=\frac{6}{16}
=3/8
$