4(2x+1)(5x+13)=0

Solution for 4(2x+1)(5x+13)=0 equation:

4(2x+1)(5x+13)=0

We multiply parentheses ..

4(+10x^2+26x+5x+13)=0

We multiply parentheses

40x^2+104x+20x+52=0

We add all the numbers together, and all the variables

40x^2+124x+52=0

a = 40; b = 124; c = +52;
Δ = b2-4ac
Δ = 1242-4·40·52
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-84}{2*40}=\frac{-208}{80}
=-2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+84}{2*40}=\frac{-40}{80}
=-1/2
$