1000x(9x-10)=50(976+100x)

Solution for 1000x(9x-10)=50(976+100x) equation:

1000x(9x-10)=50(976+100x)

We move all terms to the left:

1000x(9x-10)-(50(976+100x))=0

We add all the numbers together, and all the variables

1000x(9x-10)-(50(100x+976))=0

We multiply parentheses

9000x^2-10000x-(50(100x+976))=0


We calculate terms in parentheses: -(50(100x+976)), so:

50(100x+976)

We multiply parentheses

5000x+48800

Back to the equation:

-(5000x+48800)


We get rid of parentheses

9000x^2-10000x-5000x-48800=0

We add all the numbers together, and all the variables

9000x^2-15000x-48800=0

a = 9000; b = -15000; c = -48800;
Δ = b2-4ac
Δ = -150002-4·9000·(-48800)
Δ = 1981800000
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:

$\sqrt{\Delta}=\sqrt{1981800000}=\sqrt{360000*5505}=\sqrt{360000}*\sqrt{5505}=600\sqrt{5505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-600\sqrt{5505}}{2*9000}=\frac{15000-600\sqrt{5505}}{18000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+600\sqrt{5505}}{2*9000}=\frac{15000+600\sqrt{5505}}{18000}
$