-7x(x+3)=-2(x+3)-5x

Solution for -7x(x+3)=-2(x+3)-5x equation:

-7x(x+3)=-2(x+3)-5x

We move all terms to the left:

-7x(x+3)-(-2(x+3)-5x)=0

We multiply parentheses

-7x^2-21x-(-2(x+3)-5x)=0


We calculate terms in parentheses: -(-2(x+3)-5x), so:

-2(x+3)-5x

We add all the numbers together, and all the variables

-5x-2(x+3)

We multiply parentheses

-5x-2x-6

We add all the numbers together, and all the variables

-7x-6

Back to the equation:

-(-7x-6)


We get rid of parentheses

-7x^2-21x+7x+6=0

We add all the numbers together, and all the variables

-7x^2-14x+6=0

a = -7; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·(-7)·6
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{91}}{2*-7}=\frac{14-2\sqrt{91}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{91}}{2*-7}=\frac{14+2\sqrt{91}}{-14}
$