39x(+2)=-2(x-5)

Solution for 39x(+2)=-2(x-5) equation:

39x(+2)=-2(x-5)

We move all terms to the left:

39x(+2)-(-2(x-5))=0

We add all the numbers together, and all the variables

39x2-(-2(x-5))=0

We add all the numbers together, and all the variables

39x^2-(-2(x-5))=0


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

-2(x-5)

We multiply parentheses

-2x+10

Back to the equation:

-(-2x+10)


We get rid of parentheses

39x^2+2x-10=0

a = 39; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·39·(-10)
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{391}}{2*39}=\frac{-2-2\sqrt{391}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{391}}{2*39}=\frac{-2+2\sqrt{391}}{78}
$