2x(10x-23)+106=108

Solution for 2x(10x-23)+106=108 equation:

2x(10x-23)+106=108

We move all terms to the left:

2x(10x-23)+106-(108)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

20x^2-46x-2=0

a = 20; b = -46; c = -2;
Δ = b2-4ac
Δ = -462-4·20·(-2)
Δ = 2276
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:

$\sqrt{\Delta}=\sqrt{2276}=\sqrt{4*569}=\sqrt{4}*\sqrt{569}=2\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{569}}{2*20}=\frac{46-2\sqrt{569}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{569}}{2*20}=\frac{46+2\sqrt{569}}{40}
$