5x(2x+5)=260

Solution for 5x(2x+5)=260 equation:

5x(2x+5)=260

We move all terms to the left:

5x(2x+5)-(260)=0

We multiply parentheses

10x^2+25x-260=0

a = 10; b = 25; c = -260;
Δ = b2-4ac
Δ = 252-4·10·(-260)
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-105}{2*10}=\frac{-130}{20}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+105}{2*10}=\frac{80}{20}
=4
$