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x(x-11)+8(x+1/4)=0
We add all the numbers together, and all the variables
x(x-11)+8(+x+1/4)=0
We multiply parentheses
x^2-11x+8x+1/4*8=0
We multiply all the terms by the denominator
x^2*4*8-11x*4*8+8x*4*8+1=0
Wy multiply elements
32x^2*8-352x*8+256x*8+1=0
Wy multiply elements
256x^2-2816x+2048x+1=0
We add all the numbers together, and all the variables
256x^2-768x+1=0
a = 256; b = -768; c = +1;
Δ = b2-4ac
Δ = -7682-4·256·1
Δ = 588800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{588800}=\sqrt{25600*23}=\sqrt{25600}*\sqrt{23}=160\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-768)-160\sqrt{23}}{2*256}=\frac{768-160\sqrt{23}}{512} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-768)+160\sqrt{23}}{2*256}=\frac{768+160\sqrt{23}}{512} $
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