7(y-5)3y=10(y+1)

Solution for 7(y-5)3y=10(y+1) equation:

7(y-5)3y=10(y+1)

We move all terms to the left:

7(y-5)3y-(10(y+1))=0

We multiply parentheses

21y^2-105y-(10(y+1))=0


We calculate terms in parentheses: -(10(y+1)), so:

10(y+1)

We multiply parentheses

10y+10

Back to the equation:

-(10y+10)


We get rid of parentheses

21y^2-105y-10y-10=0

We add all the numbers together, and all the variables

21y^2-115y-10=0

a = 21; b = -115; c = -10;
Δ = b2-4ac
Δ = -1152-4·21·(-10)
Δ = 14065
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{-(-115)-\sqrt{14065}}{2*21}=\frac{115-\sqrt{14065}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+\sqrt{14065}}{2*21}=\frac{115+\sqrt{14065}}{42}
$