4y^2=7y+2=0

Solution for 4y^2=7y+2=0 equation:

4y^2=7y+2=0

We move all terms to the left:

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

We get rid of parentheses

4y^2-7y-2=0

a = 4; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·4·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*4}=\frac{-2}{8}
=-1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*4}=\frac{16}{8}
=2
$