x=7/12x+600

Solution for x=7/12x+600 equation:

x=7/12x+600

We move all terms to the left:

x-(7/12x+600)=0


Domain of the equation: 12x+600)!=0

x∈R


We get rid of parentheses

x-7/12x-600=0

We multiply all the terms by the denominator


x*12x-600*12x-7=0

Wy multiply elements

12x^2-7200x-7=0

a = 12; b = -7200; c = -7;
Δ = b2-4ac
Δ = -72002-4·12·(-7)
Δ = 51840336
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:

$\sqrt{\Delta}=\sqrt{51840336}=\sqrt{16*3240021}=\sqrt{16}*\sqrt{3240021}=4\sqrt{3240021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7200)-4\sqrt{3240021}}{2*12}=\frac{7200-4\sqrt{3240021}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7200)+4\sqrt{3240021}}{2*12}=\frac{7200+4\sqrt{3240021}}{24}
$