13b-6/2b=30

Solution for 13b-6/2b=30 equation:

13b-6/2b=30

We move all terms to the left:

13b-6/2b-(30)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


13b*2b-30*2b-6=0

Wy multiply elements

26b^2-60b-6=0

a = 26; b = -60; c = -6;
Δ = b2-4ac
Δ = -602-4·26·(-6)
Δ = 4224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{66}}{2*26}=\frac{60-8\sqrt{66}}{52}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{66}}{2*26}=\frac{60+8\sqrt{66}}{52}
$