4x(2x+13)=80

Solution for 4x(2x+13)=80 equation:

4x(2x+13)=80

We move all terms to the left:

4x(2x+13)-(80)=0

We multiply parentheses

8x^2+52x-80=0

a = 8; b = 52; c = -80;
Δ = b2-4ac
Δ = 522-4·8·(-80)
Δ = 5264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5264}=\sqrt{16*329}=\sqrt{16}*\sqrt{329}=4\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{329}}{2*8}=\frac{-52-4\sqrt{329}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{329}}{2*8}=\frac{-52+4\sqrt{329}}{16}
$