(4x+15)(2x+65)=180

Solution for (4x+15)(2x+65)=180 equation:

(4x+15)(2x+65)=180

We move all terms to the left:

(4x+15)(2x+65)-(180)=0

We multiply parentheses ..

(+8x^2+260x+30x+975)-180=0

We get rid of parentheses

8x^2+260x+30x+975-180=0

We add all the numbers together, and all the variables

8x^2+290x+795=0

a = 8; b = 290; c = +795;
Δ = b2-4ac
Δ = 2902-4·8·795
Δ = 58660
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:

$\sqrt{\Delta}=\sqrt{58660}=\sqrt{4*14665}=\sqrt{4}*\sqrt{14665}=2\sqrt{14665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(290)-2\sqrt{14665}}{2*8}=\frac{-290-2\sqrt{14665}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(290)+2\sqrt{14665}}{2*8}=\frac{-290+2\sqrt{14665}}{16}
$