(4x+3)(4x+7)=180

Solution for (4x+3)(4x+7)=180 equation:

(4x+3)(4x+7)=180

We move all terms to the left:

(4x+3)(4x+7)-(180)=0

We multiply parentheses ..

(+16x^2+28x+12x+21)-180=0

We get rid of parentheses

16x^2+28x+12x+21-180=0

We add all the numbers together, and all the variables

16x^2+40x-159=0

a = 16; b = 40; c = -159;
Δ = b2-4ac
Δ = 402-4·16·(-159)
Δ = 11776
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:

$\sqrt{\Delta}=\sqrt{11776}=\sqrt{256*46}=\sqrt{256}*\sqrt{46}=16\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{46}}{2*16}=\frac{-40-16\sqrt{46}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{46}}{2*16}=\frac{-40+16\sqrt{46}}{32}
$