(5y+21)(7y+29)=0

Solution for (5y+21)(7y+29)=0 equation:

(5y+21)(7y+29)=0

We multiply parentheses ..

(+35y^2+145y+147y+609)=0

We get rid of parentheses

35y^2+145y+147y+609=0

We add all the numbers together, and all the variables

35y^2+292y+609=0

a = 35; b = 292; c = +609;
Δ = b2-4ac
Δ = 2922-4·35·609
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(292)-2}{2*35}=\frac{-294}{70}
=-4+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(292)+2}{2*35}=\frac{-290}{70}
=-4+1/7
$