(7x+9)(4x+4)+57=180

Solution for (7x+9)(4x+4)+57=180 equation:

(7x+9)(4x+4)+57=180

We move all terms to the left:

(7x+9)(4x+4)+57-(180)=0

We add all the numbers together, and all the variables

(7x+9)(4x+4)-123=0

We multiply parentheses ..

(+28x^2+28x+36x+36)-123=0

We get rid of parentheses

28x^2+28x+36x+36-123=0

We add all the numbers together, and all the variables

28x^2+64x-87=0

a = 28; b = 64; c = -87;
Δ = b2-4ac
Δ = 642-4·28·(-87)
Δ = 13840
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:

$\sqrt{\Delta}=\sqrt{13840}=\sqrt{16*865}=\sqrt{16}*\sqrt{865}=4\sqrt{865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{865}}{2*28}=\frac{-64-4\sqrt{865}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{865}}{2*28}=\frac{-64+4\sqrt{865}}{56}
$