(4x+5)3x=2

Solution for (4x+5)3x=2 equation:

(4x+5)3x=2

We move all terms to the left:

(4x+5)3x-(2)=0

We multiply parentheses

12x^2+15x-2=0

a = 12; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·12·(-2)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{321}}{2*12}=\frac{-15-\sqrt{321}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{321}}{2*12}=\frac{-15+\sqrt{321}}{24}
$