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2(x-4)x=-6x+9x+4=
We move all terms to the left:
2(x-4)x-(-6x+9x+4)=0
We add all the numbers together, and all the variables
2(x-4)x-(3x+4)=0
We multiply parentheses
2x^2-8x-(3x+4)=0
We get rid of parentheses
2x^2-8x-3x-4=0
We add all the numbers together, and all the variables
2x^2-11x-4=0
a = 2; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·2·(-4)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{17}}{2*2}=\frac{11-3\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{17}}{2*2}=\frac{11+3\sqrt{17}}{4} $
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