25x2+10-(12-8x)+4x-(30-8x)=(5x+1)2

Solution for 25x2+10-(12-8x)+4x-(30-8x)=(5x+1)2 equation:

25x^2+10-(12-8x)+4x-(30-8x)=(5x+1)2

We move all terms to the left:

25x^2+10-(12-8x)+4x-(30-8x)-((5x+1)2)=0

We add all the numbers together, and all the variables

25x^2-(-8x+12)+4x-(-8x+30)-((5x+1)2)+10=0

We add all the numbers together, and all the variables

25x^2+4x-(-8x+12)-(-8x+30)-((5x+1)2)+10=0

We get rid of parentheses

25x^2+4x+8x+8x-((5x+1)2)-12-30+10=0


We calculate terms in parentheses: -((5x+1)2), so:

(5x+1)2

We multiply parentheses

10x+2

Back to the equation:

-(10x+2)


We add all the numbers together, and all the variables

25x^2+20x-(10x+2)-32=0

We get rid of parentheses

25x^2+20x-10x-2-32=0

We add all the numbers together, and all the variables

25x^2+10x-34=0

a = 25; b = 10; c = -34;
Δ = b2-4ac
Δ = 102-4·25·(-34)
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{35}}{2*25}=\frac{-10-10\sqrt{35}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{35}}{2*25}=\frac{-10+10\sqrt{35}}{50}
$