X-47/70x=13

Solution for X-47/70x=13 equation:

X-47/70X=13

We move all terms to the left:

X-47/70X-(13)=0


Domain of the equation: 70X!=0

X!=0/70

X!=0

X∈R


We multiply all the terms by the denominator


X*70X-13*70X-47=0

Wy multiply elements

70X^2-910X-47=0

a = 70; b = -910; c = -47;
Δ = b2-4ac
Δ = -9102-4·70·(-47)
Δ = 841260
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:

$\sqrt{\Delta}=\sqrt{841260}=\sqrt{4*210315}=\sqrt{4}*\sqrt{210315}=2\sqrt{210315}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-910)-2\sqrt{210315}}{2*70}=\frac{910-2\sqrt{210315}}{140}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-910)+2\sqrt{210315}}{2*70}=\frac{910+2\sqrt{210315}}{140}
$