4(2x-1)=-10x(x-5)

Solution for 4(2x-1)=-10x(x-5) equation:

4(2x-1)=-10x(x-5)

We move all terms to the left:

4(2x-1)-(-10x(x-5))=0

We multiply parentheses

8x-(-10x(x-5))-4=0


We calculate terms in parentheses: -(-10x(x-5)), so:

-10x(x-5)

We multiply parentheses

-10x^2+50x

Back to the equation:

-(-10x^2+50x)


We get rid of parentheses

10x^2-50x+8x-4=0

We add all the numbers together, and all the variables

10x^2-42x-4=0

a = 10; b = -42; c = -4;
Δ = b2-4ac
Δ = -422-4·10·(-4)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{481}}{2*10}=\frac{42-2\sqrt{481}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{481}}{2*10}=\frac{42+2\sqrt{481}}{20}
$