(4x+3)4x+1=180

Solution for (4x+3)4x+1=180 equation:

(4x+3)4x+1=180

We move all terms to the left:

(4x+3)4x+1-(180)=0

We add all the numbers together, and all the variables

(4x+3)4x-179=0

We multiply parentheses

16x^2+12x-179=0

a = 16; b = 12; c = -179;
Δ = b2-4ac
Δ = 122-4·16·(-179)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{29}}{2*16}=\frac{-12-20\sqrt{29}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{29}}{2*16}=\frac{-12+20\sqrt{29}}{32}
$