35(x+2)=25(4-x2)

Solution for 35(x+2)=25(4-x2) equation:

35(x+2)=25(4-x2)

We move all terms to the left:

35(x+2)-(25(4-x2))=0

We add all the numbers together, and all the variables

-(25(-1x^2+4))+35(x+2)=0

We multiply parentheses

-(25(-1x^2+4))+35x+70=0


We calculate terms in parentheses: -(25(-1x^2+4)), so:

25(-1x^2+4)

We multiply parentheses

-25x^2+100

Back to the equation:

-(-25x^2+100)


We get rid of parentheses

25x^2+35x-100+70=0

We add all the numbers together, and all the variables

25x^2+35x-30=0

a = 25; b = 35; c = -30;
Δ = b2-4ac
Δ = 352-4·25·(-30)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-65}{2*25}=\frac{-100}{50}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+65}{2*25}=\frac{30}{50}
=3/5
$