(2x-10)(65-x)=180

Solution for (2x-10)(65-x)=180 equation:

(2x-10)(65-x)=180

We move all terms to the left:

(2x-10)(65-x)-(180)=0

We add all the numbers together, and all the variables

(2x-10)(-1x+65)-180=0

We multiply parentheses ..

(-2x^2+130x+10x-650)-180=0

We get rid of parentheses

-2x^2+130x+10x-650-180=0

We add all the numbers together, and all the variables

-2x^2+140x-830=0

a = -2; b = 140; c = -830;
Δ = b2-4ac
Δ = 1402-4·(-2)·(-830)
Δ = 12960
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:

$\sqrt{\Delta}=\sqrt{12960}=\sqrt{1296*10}=\sqrt{1296}*\sqrt{10}=36\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-36\sqrt{10}}{2*-2}=\frac{-140-36\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+36\sqrt{10}}{2*-2}=\frac{-140+36\sqrt{10}}{-4}
$