51x(x+3)+9x-23=20(4x+8)

Solution for 51x(x+3)+9x-23=20(4x+8) equation:

51x(x+3)+9x-23=20(4x+8)

We move all terms to the left:

51x(x+3)+9x-23-(20(4x+8))=0

We add all the numbers together, and all the variables

9x+51x(x+3)-(20(4x+8))-23=0

We multiply parentheses

51x^2+9x+153x-(20(4x+8))-23=0


We calculate terms in parentheses: -(20(4x+8)), so:

20(4x+8)

We multiply parentheses

80x+160

Back to the equation:

-(80x+160)


We add all the numbers together, and all the variables

51x^2+162x-(80x+160)-23=0

We get rid of parentheses

51x^2+162x-80x-160-23=0

We add all the numbers together, and all the variables

51x^2+82x-183=0

a = 51; b = 82; c = -183;
Δ = b2-4ac
Δ = 822-4·51·(-183)
Δ = 44056
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:

$\sqrt{\Delta}=\sqrt{44056}=\sqrt{4*11014}=\sqrt{4}*\sqrt{11014}=2\sqrt{11014}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{11014}}{2*51}=\frac{-82-2\sqrt{11014}}{102}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{11014}}{2*51}=\frac{-82+2\sqrt{11014}}{102}
$