4(4x+2)=-5(5x-5)4x

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

4(4x+2)=-5(5x-5)4x

We move all terms to the left:

4(4x+2)-(-5(5x-5)4x)=0

We multiply parentheses

16x-(-5(5x-5)4x)+8=0


We calculate terms in parentheses: -(-5(5x-5)4x), so:

-5(5x-5)4x

We multiply parentheses

-100x^2+100x

Back to the equation:

-(-100x^2+100x)


We get rid of parentheses

100x^2-100x+16x+8=0

We add all the numbers together, and all the variables

100x^2-84x+8=0

a = 100; b = -84; c = +8;
Δ = b2-4ac
Δ = -842-4·100·8
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{241}}{2*100}=\frac{84-4\sqrt{241}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{241}}{2*100}=\frac{84+4\sqrt{241}}{200}
$