4x(3+2x)+7=38

Solution for 4x(3+2x)+7=38 equation:

4x(3+2x)+7=38

We move all terms to the left:

4x(3+2x)+7-(38)=0

We add all the numbers together, and all the variables

4x(2x+3)+7-38=0

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+12x-31=0

a = 8; b = 12; c = -31;
Δ = b2-4ac
Δ = 122-4·8·(-31)
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{71}}{2*8}=\frac{-12-4\sqrt{71}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{71}}{2*8}=\frac{-12+4\sqrt{71}}{16}
$