10(y2)=3(y+8)

Solution for 10(y2)=3(y+8) equation:

10(y2)=3(y+8)

We move all terms to the left:

10(y2)-(3(y+8))=0

We add all the numbers together, and all the variables

10y^2-(3(y+8))=0


We calculate terms in parentheses: -(3(y+8)), so:

3(y+8)

We multiply parentheses

3y+24

Back to the equation:

-(3y+24)


We get rid of parentheses

10y^2-3y-24=0

a = 10; b = -3; c = -24;
Δ = b2-4ac
Δ = -32-4·10·(-24)
Δ = 969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{969}}{2*10}=\frac{3-\sqrt{969}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{969}}{2*10}=\frac{3+\sqrt{969}}{20}
$