(9x+65)(5x+97)=180

Solution for (9x+65)(5x+97)=180 equation:

(9x+65)(5x+97)=180

We move all terms to the left:

(9x+65)(5x+97)-(180)=0

We multiply parentheses ..

(+45x^2+873x+325x+6305)-180=0

We get rid of parentheses

45x^2+873x+325x+6305-180=0

We add all the numbers together, and all the variables

45x^2+1198x+6125=0

a = 45; b = 1198; c = +6125;
Δ = b2-4ac
Δ = 11982-4·45·6125
Δ = 332704
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:

$\sqrt{\Delta}=\sqrt{332704}=\sqrt{16*20794}=\sqrt{16}*\sqrt{20794}=4\sqrt{20794}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1198)-4\sqrt{20794}}{2*45}=\frac{-1198-4\sqrt{20794}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1198)+4\sqrt{20794}}{2*45}=\frac{-1198+4\sqrt{20794}}{90}
$