5x(10x-9)=6x(2x+16)

Solution for 5x(10x-9)=6x(2x+16) equation:

5x(10x-9)=6x(2x+16)

We move all terms to the left:

5x(10x-9)-(6x(2x+16))=0

We multiply parentheses

50x^2-45x-(6x(2x+16))=0


We calculate terms in parentheses: -(6x(2x+16)), so:

6x(2x+16)

We multiply parentheses

12x^2+96x

Back to the equation:

-(12x^2+96x)


We get rid of parentheses

50x^2-12x^2-45x-96x=0

We add all the numbers together, and all the variables

38x^2-141x=0

a = 38; b = -141; c = 0;
Δ = b2-4ac
Δ = -1412-4·38·0
Δ = 19881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19881}=141$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-141)-141}{2*38}=\frac{0}{76}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-141)+141}{2*38}=\frac{282}{76}
=3+27/38
$