4y^2-3y=45

Solution for 4y^2-3y=45 equation:

4y^2-3y=45

We move all terms to the left:

4y^2-3y-(45)=0

a = 4; b = -3; c = -45;
Δ = b2-4ac
Δ = -32-4·4·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*4}=\frac{-24}{8}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*4}=\frac{30}{8}
=3+3/4
$