14y+22-15y^2+23=0

Solution for 14y+22-15y^2+23=0 equation:

14y+22-15y^2+23=0

We add all the numbers together, and all the variables

-15y^2+14y+45=0

a = -15; b = 14; c = +45;
Δ = b2-4ac
Δ = 142-4·(-15)·45
Δ = 2896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{181}}{2*-15}=\frac{-14-4\sqrt{181}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{181}}{2*-15}=\frac{-14+4\sqrt{181}}{-30}
$