x(10x+1)=24

Solution for x(10x+1)=24 equation:

x(10x+1)=24

We move all terms to the left:

x(10x+1)-(24)=0

We multiply parentheses

10x^2+x-24=0

a = 10; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·10·(-24)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*10}=\frac{-32}{20}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*10}=\frac{30}{20}
=1+1/2
$