9y^2+4=y^2+10y+7

Solution for 9y^2+4=y^2+10y+7 equation:

9y^2+4=y^2+10y+7

We move all terms to the left:

9y^2+4-(y^2+10y+7)=0

We get rid of parentheses

9y^2-y^2-10y-7+4=0

We add all the numbers together, and all the variables

8y^2-10y-3=0

a = 8; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·8·(-3)
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*8}=\frac{-4}{16}
=-1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*8}=\frac{24}{16}
=1+1/2
$