X(5-0.05x)-1.50x=60

Solution for X(5-0.05x)-1.50x=60 equation:

X(5-0.05X)-1.50X=60

We move all terms to the left:

X(5-0.05X)-1.50X-(60)=0

We add all the numbers together, and all the variables

X(-0.05X+5)-1.50X-60=0

We add all the numbers together, and all the variables

-1.5X+X(-0.05X+5)-60=0

We multiply parentheses

0X^2-1.5X+5X-60=0

We add all the numbers together, and all the variables

X^2+3.5X-60=0

a = 1; b = 3.5; c = -60;
Δ = b2-4ac
Δ = 3.52-4·1·(-60)
Δ = 252.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3.5)-\sqrt{252.25}}{2*1}=\frac{-3.5-\sqrt{252.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{252.25}}{2*1}=\frac{-3.5+\sqrt{252.25}}{2}
$