4x(2x+1)=7

Solution for 4x(2x+1)=7 equation:

4x(2x+1)=7

We move all terms to the left:

4x(2x+1)-(7)=0

We multiply parentheses

8x^2+4x-7=0

a = 8; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·8·(-7)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{15}}{2*8}=\frac{-4-4\sqrt{15}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{15}}{2*8}=\frac{-4+4\sqrt{15}}{16}
$