4x(x+30)=(5x+-25)

Solution for 4x(x+30)=(5x+-25) equation:

4x(x+30)=(5x+-25)

We move all terms to the left:

4x(x+30)-((5x+-25))=0

We add all the numbers together, and all the variables

4x(x+30)-((5x-25))=0

We multiply parentheses

4x^2+120x-((5x-25))=0


We calculate terms in parentheses: -((5x-25)), so:

(5x-25)

We get rid of parentheses

5x-25

Back to the equation:

-(5x-25)


We get rid of parentheses

4x^2+120x-5x+25=0

We add all the numbers together, and all the variables

4x^2+115x+25=0

a = 4; b = 115; c = +25;
Δ = b2-4ac
Δ = 1152-4·4·25
Δ = 12825
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:

$\sqrt{\Delta}=\sqrt{12825}=\sqrt{225*57}=\sqrt{225}*\sqrt{57}=15\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-15\sqrt{57}}{2*4}=\frac{-115-15\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+15\sqrt{57}}{2*4}=\frac{-115+15\sqrt{57}}{8}
$