(4x-5)(2x+6)=0

Solution for (4x-5)(2x+6)=0 equation:

(4x-5)(2x+6)=0

We multiply parentheses ..

(+8x^2+24x-10x-30)=0

We get rid of parentheses

8x^2+24x-10x-30=0

We add all the numbers together, and all the variables

8x^2+14x-30=0

a = 8; b = 14; c = -30;
Δ = b2-4ac
Δ = 142-4·8·(-30)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*8}=\frac{20}{16}
=1+1/4
$