5x-13=-21(x-4)x

Solution for 5x-13=-21(x-4)x equation:

5x-13=-21(x-4)x

We move all terms to the left:

5x-13-(-21(x-4)x)=0


We calculate terms in parentheses: -(-21(x-4)x), so:

-21(x-4)x

We multiply parentheses

-21x^2+84x

Back to the equation:

-(-21x^2+84x)


We get rid of parentheses

21x^2-84x+5x-13=0

We add all the numbers together, and all the variables

21x^2-79x-13=0

a = 21; b = -79; c = -13;
Δ = b2-4ac
Δ = -792-4·21·(-13)
Δ = 7333
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-\sqrt{7333}}{2*21}=\frac{79-\sqrt{7333}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{7333}}{2*21}=\frac{79+\sqrt{7333}}{42}
$