(4x+25)(8x+5)=180

Solution for (4x+25)(8x+5)=180 equation:

(4x+25)(8x+5)=180

We move all terms to the left:

(4x+25)(8x+5)-(180)=0

We multiply parentheses ..

(+32x^2+20x+200x+125)-180=0

We get rid of parentheses

32x^2+20x+200x+125-180=0

We add all the numbers together, and all the variables

32x^2+220x-55=0

a = 32; b = 220; c = -55;
Δ = b2-4ac
Δ = 2202-4·32·(-55)
Δ = 55440
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:

$\sqrt{\Delta}=\sqrt{55440}=\sqrt{144*385}=\sqrt{144}*\sqrt{385}=12\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-12\sqrt{385}}{2*32}=\frac{-220-12\sqrt{385}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+12\sqrt{385}}{2*32}=\frac{-220+12\sqrt{385}}{64}
$