0.5h+13(h-6)=5/6h+2

Solution for 0.5h+13(h-6)=5/6h+2 equation:

0.5h+13(h-6)=5/6h+2

We move all terms to the left:

0.5h+13(h-6)-(5/6h+2)=0


Domain of the equation: 6h+2)!=0

h∈R


We multiply parentheses

0.5h+13h-(5/6h+2)-78=0

We get rid of parentheses

0.5h+13h-5/6h-2-78=0

We multiply all the terms by the denominator


(0.5h)*6h+13h*6h-2*6h-78*6h-5=0

We add all the numbers together, and all the variables

(+0.5h)*6h+13h*6h-2*6h-78*6h-5=0

We multiply parentheses

0h^2+13h*6h-2*6h-78*6h-5=0

Wy multiply elements

0h^2+78h^2-12h-468h-5=0

We add all the numbers together, and all the variables

79h^2-480h-5=0

a = 79; b = -480; c = -5;
Δ = b2-4ac
Δ = -4802-4·79·(-5)
Δ = 231980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{231980}=\sqrt{4*57995}=\sqrt{4}*\sqrt{57995}=2\sqrt{57995}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57995}}{2*79}=\frac{480-2\sqrt{57995}}{158}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57995}}{2*79}=\frac{480+2\sqrt{57995}}{158}
$