4(2x+5)10x=-(8-12x)

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

4(2x+5)10x=-(8-12x)

We move all terms to the left:

4(2x+5)10x-(-(8-12x))=0

We add all the numbers together, and all the variables

4(2x+5)10x-(-(-12x+8))=0

We multiply parentheses

80x^2+200x-(-(-12x+8))=0


We calculate terms in parentheses: -(-(-12x+8)), so:

-(-12x+8)

We get rid of parentheses

12x-8

Back to the equation:

-(12x-8)


We get rid of parentheses

80x^2+200x-12x+8=0

We add all the numbers together, and all the variables

80x^2+188x+8=0

a = 80; b = 188; c = +8;
Δ = b2-4ac
Δ = 1882-4·80·8
Δ = 32784
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:

$\sqrt{\Delta}=\sqrt{32784}=\sqrt{16*2049}=\sqrt{16}*\sqrt{2049}=4\sqrt{2049}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188)-4\sqrt{2049}}{2*80}=\frac{-188-4\sqrt{2049}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188)+4\sqrt{2049}}{2*80}=\frac{-188+4\sqrt{2049}}{160}
$