12x-3/10x+7=1

Solution for 12x-3/10x+7=1 equation:

12x-3/10x+7=1

We move all terms to the left:

12x-3/10x+7-(1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

12x-3/10x+6=0

We multiply all the terms by the denominator


12x*10x+6*10x-3=0

Wy multiply elements

120x^2+60x-3=0

a = 120; b = 60; c = -3;
Δ = b2-4ac
Δ = 602-4·120·(-3)
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{35}}{2*120}=\frac{-60-12\sqrt{35}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{35}}{2*120}=\frac{-60+12\sqrt{35}}{240}
$