x-5(x+2)=2(x+4)x-7

Solution for x-5(x+2)=2(x+4)x-7 equation:

x-5(x+2)=2(x+4)x-7

We move all terms to the left:

x-5(x+2)-(2(x+4)x-7)=0

We multiply parentheses

x-5x-(2(x+4)x-7)-10=0


We calculate terms in parentheses: -(2(x+4)x-7), so:

2(x+4)x-7

We multiply parentheses

2x^2+8x-7

Back to the equation:

-(2x^2+8x-7)


We add all the numbers together, and all the variables

-4x-(2x^2+8x-7)-10=0

We get rid of parentheses

-2x^2-4x-8x+7-10=0

We add all the numbers together, and all the variables

-2x^2-12x-3=0

a = -2; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·(-2)·(-3)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-2}=\frac{12-2\sqrt{30}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-2}=\frac{12+2\sqrt{30}}{-4}
$