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}
$