y(y+3)=7y+10

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

y(y+3)=7y+10

We move all terms to the left:

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

We multiply parentheses

y^2+3y-(7y+10)=0

We get rid of parentheses

y^2+3y-7y-10=0

We add all the numbers together, and all the variables

y^2-4y-10=0

a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2}
$