x=1/3;12x+7

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

x=1/312x+7

We move all terms to the left:

x-(1/312x+7)=0


Domain of the equation: 312x+7)!=0

x∈R


We get rid of parentheses

x-1/312x-7=0

We multiply all the terms by the denominator


x*312x-7*312x-1=0

Wy multiply elements

312x^2-2184x-1=0

a = 312; b = -2184; c = -1;
Δ = b2-4ac
Δ = -21842-4·312·(-1)
Δ = 4771104
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:

$\sqrt{\Delta}=\sqrt{4771104}=\sqrt{16*298194}=\sqrt{16}*\sqrt{298194}=4\sqrt{298194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2184)-4\sqrt{298194}}{2*312}=\frac{2184-4\sqrt{298194}}{624}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2184)+4\sqrt{298194}}{2*312}=\frac{2184+4\sqrt{298194}}{624}
$