(8+1/3)y+4/5=910

Solution for (8+1/3)y+4/5=910 equation:

(8+1/3)y+4/5=910

We move all terms to the left:

(8+1/3)y+4/5-(910)=0


Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


determiningTheFunctionDomain
(8+1/3)y-910+4/5=0

We add all the numbers together, and all the variables

(1/3+8)y-910+4/5=0

We multiply parentheses

y^2+8y-910+4/5=0

We multiply all the terms by the denominator


y^2*5+8y*5+4-910*5=0

We add all the numbers together, and all the variables

y^2*5+8y*5-4546=0

Wy multiply elements

5y^2+40y-4546=0

a = 5; b = 40; c = -4546;
Δ = b2-4ac
Δ = 402-4·5·(-4546)
Δ = 92520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92520}=\sqrt{36*2570}=\sqrt{36}*\sqrt{2570}=6\sqrt{2570}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-6\sqrt{2570}}{2*5}=\frac{-40-6\sqrt{2570}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+6\sqrt{2570}}{2*5}=\frac{-40+6\sqrt{2570}}{10}
$