(4y-5)(2y+5)=90

Solution for (4y-5)(2y+5)=90 equation:

(4y-5)(2y+5)=90

We move all terms to the left:

(4y-5)(2y+5)-(90)=0

We multiply parentheses ..

(+8y^2+20y-10y-25)-90=0

We get rid of parentheses

8y^2+20y-10y-25-90=0

We add all the numbers together, and all the variables

8y^2+10y-115=0

a = 8; b = 10; c = -115;
Δ = b2-4ac
Δ = 102-4·8·(-115)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{105}}{2*8}=\frac{-10-6\sqrt{105}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{105}}{2*8}=\frac{-10+6\sqrt{105}}{16}
$