(4x+5)(2x+9)=0

Solution for (4x+5)(2x+9)=0 equation:

(4x+5)(2x+9)=0

We multiply parentheses ..

(+8x^2+36x+10x+45)=0

We get rid of parentheses

8x^2+36x+10x+45=0

We add all the numbers together, and all the variables

8x^2+46x+45=0

a = 8; b = 46; c = +45;
Δ = b2-4ac
Δ = 462-4·8·45
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-26}{2*8}=\frac{-72}{16}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+26}{2*8}=\frac{-20}{16}
=-1+1/4
$