13x(10x+21)=180

Solution for 13x(10x+21)=180 equation:

13x(10x+21)=180

We move all terms to the left:

13x(10x+21)-(180)=0

We multiply parentheses

130x^2+273x-180=0

a = 130; b = 273; c = -180;
Δ = b2-4ac
Δ = 2732-4·130·(-180)
Δ = 168129
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:

$\sqrt{\Delta}=\sqrt{168129}=\sqrt{9*18681}=\sqrt{9}*\sqrt{18681}=3\sqrt{18681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(273)-3\sqrt{18681}}{2*130}=\frac{-273-3\sqrt{18681}}{260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(273)+3\sqrt{18681}}{2*130}=\frac{-273+3\sqrt{18681}}{260}
$