(2x+5)4x=12

Solution for (2x+5)4x=12 equation:

(2x+5)4x=12

We move all terms to the left:

(2x+5)4x-(12)=0

We multiply parentheses

8x^2+20x-12=0

a = 8; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·8·(-12)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-28}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*8}=\frac{8}{16}
=1/2
$