3x+7/12x=100

Solution for 3x+7/12x=100 equation:

3x+7/12x=100

We move all terms to the left:

3x+7/12x-(100)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We multiply all the terms by the denominator


3x*12x-100*12x+7=0

Wy multiply elements

36x^2-1200x+7=0

a = 36; b = -1200; c = +7;
Δ = b2-4ac
Δ = -12002-4·36·7
Δ = 1438992
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:

$\sqrt{\Delta}=\sqrt{1438992}=\sqrt{144*9993}=\sqrt{144}*\sqrt{9993}=12\sqrt{9993}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-12\sqrt{9993}}{2*36}=\frac{1200-12\sqrt{9993}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+12\sqrt{9993}}{2*36}=\frac{1200+12\sqrt{9993}}{72}
$