(6x+5)(4x+5)=180

Solution for (6x+5)(4x+5)=180 equation:

(6x+5)(4x+5)=180

We move all terms to the left:

(6x+5)(4x+5)-(180)=0

We multiply parentheses ..

(+24x^2+30x+20x+25)-180=0

We get rid of parentheses

24x^2+30x+20x+25-180=0

We add all the numbers together, and all the variables

24x^2+50x-155=0

a = 24; b = 50; c = -155;
Δ = b2-4ac
Δ = 502-4·24·(-155)
Δ = 17380
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:

$\sqrt{\Delta}=\sqrt{17380}=\sqrt{4*4345}=\sqrt{4}*\sqrt{4345}=2\sqrt{4345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{4345}}{2*24}=\frac{-50-2\sqrt{4345}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{4345}}{2*24}=\frac{-50+2\sqrt{4345}}{48}
$