2y^2+5y=4

Solution for 2y^2+5y=4 equation:

2y^2+5y=4

We move all terms to the left:

2y^2+5y-(4)=0

a = 2; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·2·(-4)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{57}}{2*2}=\frac{-5-\sqrt{57}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*2}=\frac{-5+\sqrt{57}}{4}
$