4y2=3-5y

Solution for 4y2=3-5y equation:

4y^2=3-5y

We move all terms to the left:

4y^2-(3-5y)=0

We add all the numbers together, and all the variables

4y^2-(-5y+3)=0

We get rid of parentheses

4y^2+5y-3=0

a = 4; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·4·(-3)
Δ = 73
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{73}}{2*4}=\frac{-5-\sqrt{73}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*4}=\frac{-5+\sqrt{73}}{8}
$