4y^2+3y=7

Solution for 4y^2+3y=7 equation:

4y^2+3y=7

We move all terms to the left:

4y^2+3y-(7)=0

a = 4; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·4·(-7)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-11}{2*4}=\frac{-14}{8}
=-1+3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*4}=\frac{8}{8}
=1
$