6y=-3y2+7

Solution for 6y=-3y2+7 equation:

6y=-3y^2+7

We move all terms to the left:

6y-(-3y^2+7)=0

We get rid of parentheses

3y^2+6y-7=0

a = 3; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·3·(-7)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*3}=\frac{-6-2\sqrt{30}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*3}=\frac{-6+2\sqrt{30}}{6}
$