4(x-10)+3(x+4)=(7/2)(-2x)

Solution for 4(x-10)+3(x+4)=(7/2)(-2x) equation:

4(x-10)+3(x+4)=(7/2)(-2x)

We move all terms to the left:

4(x-10)+3(x+4)-((7/2)(-2x))=0


Domain of the equation: 2)(-2x))!=0

x∈R


We add all the numbers together, and all the variables

4(x-10)+3(x+4)-((+7/2)(-2x))=0

We multiply parentheses

4x+3x-((+7/2)(-2x))-40+12=0

We multiply parentheses ..

-((-14x^2))+4x+3x-40+12=0


We calculate terms in parentheses: -((-14x^2)), so:

(-14x^2)

We get rid of parentheses

-14x^2

Back to the equation:

-(-14x^2)


We add all the numbers together, and all the variables

-(-14x^2)+7x-28=0

We get rid of parentheses

14x^2+7x-28=0

a = 14; b = 7; c = -28;
Δ = b2-4ac
Δ = 72-4·14·(-28)
Δ = 1617
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:

$\sqrt{\Delta}=\sqrt{1617}=\sqrt{49*33}=\sqrt{49}*\sqrt{33}=7\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{33}}{2*14}=\frac{-7-7\sqrt{33}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{33}}{2*14}=\frac{-7+7\sqrt{33}}{28}
$