3(x+5)=-2(-6-x)2x

Solution for 3(x+5)=-2(-6-x)2x equation:

3(x+5)=-2(-6-x)2x

We move all terms to the left:

3(x+5)-(-2(-6-x)2x)=0

We add all the numbers together, and all the variables

3(x+5)-(-2(-1x-6)2x)=0

We multiply parentheses

3x-(-2(-1x-6)2x)+15=0


We calculate terms in parentheses: -(-2(-1x-6)2x), so:

-2(-1x-6)2x

We multiply parentheses

4x^2+24x

Back to the equation:

-(4x^2+24x)


We get rid of parentheses

-4x^2+3x-24x+15=0

We add all the numbers together, and all the variables

-4x^2-21x+15=0

a = -4; b = -21; c = +15;
Δ = b2-4ac
Δ = -212-4·(-4)·15
Δ = 681
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{-(-21)-\sqrt{681}}{2*-4}=\frac{21-\sqrt{681}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{681}}{2*-4}=\frac{21+\sqrt{681}}{-8}
$