2x(10x-23)+106=360

Solution for 2x(10x-23)+106=360 equation:

2x(10x-23)+106=360

We move all terms to the left:

2x(10x-23)+106-(360)=0

We add all the numbers together, and all the variables

2x(10x-23)-254=0

We multiply parentheses

20x^2-46x-254=0

a = 20; b = -46; c = -254;
Δ = b2-4ac
Δ = -462-4·20·(-254)
Δ = 22436
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:

$\sqrt{\Delta}=\sqrt{22436}=\sqrt{4*5609}=\sqrt{4}*\sqrt{5609}=2\sqrt{5609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{5609}}{2*20}=\frac{46-2\sqrt{5609}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{5609}}{2*20}=\frac{46+2\sqrt{5609}}{40}
$