5(x-13)=10x(-2x+5)

Solution for 5(x-13)=10x(-2x+5) equation:

5(x-13)=10x(-2x+5)

We move all terms to the left:

5(x-13)-(10x(-2x+5))=0

We multiply parentheses

5x-(10x(-2x+5))-65=0


We calculate terms in parentheses: -(10x(-2x+5)), so:

10x(-2x+5)

We multiply parentheses

-20x^2+50x

Back to the equation:

-(-20x^2+50x)


We get rid of parentheses

20x^2-50x+5x-65=0

We add all the numbers together, and all the variables

20x^2-45x-65=0

a = 20; b = -45; c = -65;
Δ = b2-4ac
Δ = -452-4·20·(-65)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-85}{2*20}=\frac{-40}{40}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+85}{2*20}=\frac{130}{40}
=3+1/4
$