y(10+3y)=8

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Solution for y(10+3y)=8 equation:



y(10+3y)=8
We move all terms to the left:
y(10+3y)-(8)=0
We add all the numbers together, and all the variables
y(3y+10)-8=0
We multiply parentheses
3y^2+10y-8=0
a = 3; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·3·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*3}=\frac{-24}{6} =-4 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*3}=\frac{4}{6} =2/3 $

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