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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:We add all the numbers together, and all the variables
20(4x+8)
We multiply parentheses
80x+160
Back to the equation:
-(80x+160)
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} $
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