2(-2x+1)5x+2=-23

Solution for 2(-2x+1)5x+2=-23 equation:

2(-2x+1)5x+2=-23

We move all terms to the left:

2(-2x+1)5x+2-(-23)=0

We add all the numbers together, and all the variables

2(-2x+1)5x+25=0

We multiply parentheses

-20x^2+10x+25=0

a = -20; b = 10; c = +25;
Δ = b2-4ac
Δ = 102-4·(-20)·25
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{21}}{2*-20}=\frac{-10-10\sqrt{21}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{21}}{2*-20}=\frac{-10+10\sqrt{21}}{-40}
$