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

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

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

We move all terms to the left:

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

We multiply parentheses

8x^2+20x-(-5(5x-5))=0


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

-5(5x-5)

We multiply parentheses

-25x+25

Back to the equation:

-(-25x+25)


We get rid of parentheses

8x^2+20x+25x-25=0

We add all the numbers together, and all the variables

8x^2+45x-25=0

a = 8; b = 45; c = -25;
Δ = b2-4ac
Δ = 452-4·8·(-25)
Δ = 2825
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:

$\sqrt{\Delta}=\sqrt{2825}=\sqrt{25*113}=\sqrt{25}*\sqrt{113}=5\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{113}}{2*8}=\frac{-45-5\sqrt{113}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{113}}{2*8}=\frac{-45+5\sqrt{113}}{16}
$