5(1-x)-6(x-3x-7)=x(x-3)-2x(x+5)-2

Solution for 5(1-x)-6(x-3x-7)=x(x-3)-2x(x+5)-2 equation:

5(1-x)-6(x-3x-7)=x(x-3)-2x(x+5)-2

We move all terms to the left:

5(1-x)-6(x-3x-7)-(x(x-3)-2x(x+5)-2)=0

We add all the numbers together, and all the variables

5(-1x+1)-6(-2x-7)-(x(x-3)-2x(x+5)-2)=0

We multiply parentheses

-5x+12x-(x(x-3)-2x(x+5)-2)+5+42=0


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

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

We multiply parentheses

x^2-2x^2-3x-10x-2

We add all the numbers together, and all the variables

-1x^2-13x-2

Back to the equation:

-(-1x^2-13x-2)


We add all the numbers together, and all the variables

-(-1x^2-13x-2)+7x+47=0

We get rid of parentheses

1x^2+13x+7x+2+47=0

We add all the numbers together, and all the variables

x^2+20x+49=0

a = 1; b = 20; c = +49;
Δ = b2-4ac
Δ = 202-4·1·49
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{51}}{2*1}=\frac{-20-2\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{51}}{2*1}=\frac{-20+2\sqrt{51}}{2}
$