(x+5)2x=6

Solution for (x+5)2x=6 equation:

(x+5)2x=6

We move all terms to the left:

(x+5)2x-(6)=0

We multiply parentheses

2x^2+10x-6=0

a = 2; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·2·(-6)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{37}}{2*2}=\frac{-10-2\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{37}}{2*2}=\frac{-10+2\sqrt{37}}{4}
$