X+5/13x=48

Solution for X+5/13x=48 equation:

X+5/13X=48

We move all terms to the left:

X+5/13X-(48)=0


Domain of the equation: 13X!=0

X!=0/13

X!=0

X∈R


We multiply all the terms by the denominator


X*13X-48*13X+5=0

Wy multiply elements

13X^2-624X+5=0

a = 13; b = -624; c = +5;
Δ = b2-4ac
Δ = -6242-4·13·5
Δ = 389116
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:

$\sqrt{\Delta}=\sqrt{389116}=\sqrt{4*97279}=\sqrt{4}*\sqrt{97279}=2\sqrt{97279}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-624)-2\sqrt{97279}}{2*13}=\frac{624-2\sqrt{97279}}{26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-624)+2\sqrt{97279}}{2*13}=\frac{624+2\sqrt{97279}}{26}
$