5x(78-x)=180

Solution for 5x(78-x)=180 equation:

5x(78-x)=180

We move all terms to the left:

5x(78-x)-(180)=0

We add all the numbers together, and all the variables

5x(-1x+78)-180=0

We multiply parentheses

-5x^2+390x-180=0

a = -5; b = 390; c = -180;
Δ = b2-4ac
Δ = 3902-4·(-5)·(-180)
Δ = 148500
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:

$\sqrt{\Delta}=\sqrt{148500}=\sqrt{900*165}=\sqrt{900}*\sqrt{165}=30\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(390)-30\sqrt{165}}{2*-5}=\frac{-390-30\sqrt{165}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(390)+30\sqrt{165}}{2*-5}=\frac{-390+30\sqrt{165}}{-10}
$