(4x+5)(4x-2)=0

Solution for (4x+5)(4x-2)=0 equation:

(4x+5)(4x-2)=0

We multiply parentheses ..

(+16x^2-8x+20x-10)=0

We get rid of parentheses

16x^2-8x+20x-10=0

We add all the numbers together, and all the variables

16x^2+12x-10=0

a = 16; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·16·(-10)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*16}=\frac{-40}{32}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*16}=\frac{16}{32}
=1/2
$