x-3=2(x+5)2x+2

Solution for x-3=2(x+5)2x+2 equation:

x-3=2(x+5)2x+2

We move all terms to the left:

x-3-(2(x+5)2x+2)=0


We calculate terms in parentheses: -(2(x+5)2x+2), so:

2(x+5)2x+2

We multiply parentheses

4x^2+20x+2

Back to the equation:

-(4x^2+20x+2)


We get rid of parentheses

-4x^2+x-20x-2-3=0

We add all the numbers together, and all the variables

-4x^2-19x-5=0

a = -4; b = -19; c = -5;
Δ = b2-4ac
Δ = -192-4·(-4)·(-5)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{281}}{2*-4}=\frac{19-\sqrt{281}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{281}}{2*-4}=\frac{19+\sqrt{281}}{-8}
$