1,5x+x*x/12=100

Solution for 1,5x+x*x/12=100 equation:

1.5x+x*x/12=100

We move all terms to the left:

1.5x+x*x/12-(100)=0

We multiply all the terms by the denominator


(1.5x)*12+x*x-100*12=0

We add all the numbers together, and all the variables

(+1.5x)*12+x*x-100*12=0

We add all the numbers together, and all the variables

(+1.5x)*12+x*x-1200=0

We multiply parentheses

12x+x*x-1200=0

Wy multiply elements

x^2+12x-1200=0

a = 1; b = 12; c = -1200;
Δ = b2-4ac
Δ = 122-4·1·(-1200)
Δ = 4944
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:

$\sqrt{\Delta}=\sqrt{4944}=\sqrt{16*309}=\sqrt{16}*\sqrt{309}=4\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{309}}{2*1}=\frac{-12-4\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{309}}{2*1}=\frac{-12+4\sqrt{309}}{2}
$