x(x-13)=5x^2-10(5x+3)

Solution for x(x-13)=5x^2-10(5x+3) equation:

x(x-13)=5x^2-10(5x+3)

We move all terms to the left:

x(x-13)-(5x^2-10(5x+3))=0

We multiply parentheses

x^2-13x-(5x^2-10(5x+3))=0


We calculate terms in parentheses: -(5x^2-10(5x+3)), so:

5x^2-10(5x+3)

We multiply parentheses

5x^2-50x-30

Back to the equation:

-(5x^2-50x-30)


We get rid of parentheses

x^2-5x^2-13x+50x+30=0

We add all the numbers together, and all the variables

-4x^2+37x+30=0

a = -4; b = 37; c = +30;
Δ = b2-4ac
Δ = 372-4·(-4)·30
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-43}{2*-4}=\frac{-80}{-8}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+43}{2*-4}=\frac{6}{-8}
=-3/4
$