10x(20-x)+9x=2x(x+1)-126

Solution for 10x(20-x)+9x=2x(x+1)-126 equation:

10x(20-x)+9x=2x(x+1)-126

We move all terms to the left:

10x(20-x)+9x-(2x(x+1)-126)=0

We add all the numbers together, and all the variables

10x(-1x+20)+9x-(2x(x+1)-126)=0

We add all the numbers together, and all the variables

9x+10x(-1x+20)-(2x(x+1)-126)=0

We multiply parentheses

-10x^2+9x+200x-(2x(x+1)-126)=0


We calculate terms in parentheses: -(2x(x+1)-126), so:

2x(x+1)-126

We multiply parentheses

2x^2+2x-126

Back to the equation:

-(2x^2+2x-126)


We add all the numbers together, and all the variables

-10x^2+209x-(2x^2+2x-126)=0

We get rid of parentheses

-10x^2-2x^2+209x-2x+126=0

We add all the numbers together, and all the variables

-12x^2+207x+126=0

a = -12; b = 207; c = +126;
Δ = b2-4ac
Δ = 2072-4·(-12)·126
Δ = 48897
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:

$\sqrt{\Delta}=\sqrt{48897}=\sqrt{9*5433}=\sqrt{9}*\sqrt{5433}=3\sqrt{5433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(207)-3\sqrt{5433}}{2*-12}=\frac{-207-3\sqrt{5433}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(207)+3\sqrt{5433}}{2*-12}=\frac{-207+3\sqrt{5433}}{-24}
$