(2x+5)(4x+7)=180

Solution for (2x+5)(4x+7)=180 equation:

(2x+5)(4x+7)=180

We move all terms to the left:

(2x+5)(4x+7)-(180)=0

We multiply parentheses ..

(+8x^2+14x+20x+35)-180=0

We get rid of parentheses

8x^2+14x+20x+35-180=0

We add all the numbers together, and all the variables

8x^2+34x-145=0

a = 8; b = 34; c = -145;
Δ = b2-4ac
Δ = 342-4·8·(-145)
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-6\sqrt{161}}{2*8}=\frac{-34-6\sqrt{161}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+6\sqrt{161}}{2*8}=\frac{-34+6\sqrt{161}}{16}
$