X(2x+6)=71

Solution for X(2x+6)=71 equation:

X(2X+6)=71

We move all terms to the left:

X(2X+6)-(71)=0

We multiply parentheses

2X^2+6X-71=0

a = 2; b = 6; c = -71;
Δ = b2-4ac
Δ = 62-4·2·(-71)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{151}}{2*2}=\frac{-6-2\sqrt{151}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{151}}{2*2}=\frac{-6+2\sqrt{151}}{4}
$