35y^2=4-23y

Solution for 35y^2=4-23y equation:

35y^2=4-23y

We move all terms to the left:

35y^2-(4-23y)=0

We add all the numbers together, and all the variables

35y^2-(-23y+4)=0

We get rid of parentheses

35y^2+23y-4=0

a = 35; b = 23; c = -4;
Δ = b2-4ac
Δ = 232-4·35·(-4)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-33}{2*35}=\frac{-56}{70}
=-4/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+33}{2*35}=\frac{10}{70}
=1/7
$