(8y+1)(6y+5)=90

Solution for (8y+1)(6y+5)=90 equation:

(8y+1)(6y+5)=90

We move all terms to the left:

(8y+1)(6y+5)-(90)=0

We multiply parentheses ..

(+48y^2+40y+6y+5)-90=0

We get rid of parentheses

48y^2+40y+6y+5-90=0

We add all the numbers together, and all the variables

48y^2+46y-85=0

a = 48; b = 46; c = -85;
Δ = b2-4ac
Δ = 462-4·48·(-85)
Δ = 18436
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:

$\sqrt{\Delta}=\sqrt{18436}=\sqrt{4*4609}=\sqrt{4}*\sqrt{4609}=2\sqrt{4609}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{4609}}{2*48}=\frac{-46-2\sqrt{4609}}{96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{4609}}{2*48}=\frac{-46+2\sqrt{4609}}{96}
$