(19y+8)(7y+10)=22

Solution for (19y+8)(7y+10)=22 equation:

(19y+8)(7y+10)=22

We move all terms to the left:

(19y+8)(7y+10)-(22)=0

We multiply parentheses ..

(+133y^2+190y+56y+80)-22=0

We get rid of parentheses

133y^2+190y+56y+80-22=0

We add all the numbers together, and all the variables

133y^2+246y+58=0

a = 133; b = 246; c = +58;
Δ = b2-4ac
Δ = 2462-4·133·58
Δ = 29660
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:

$\sqrt{\Delta}=\sqrt{29660}=\sqrt{4*7415}=\sqrt{4}*\sqrt{7415}=2\sqrt{7415}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(246)-2\sqrt{7415}}{2*133}=\frac{-246-2\sqrt{7415}}{266}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(246)+2\sqrt{7415}}{2*133}=\frac{-246+2\sqrt{7415}}{266}
$