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4x.5(x-12)+8x=12x-9
We move all terms to the left:
4x.5(x-12)+8x-(12x-9)=0
We add all the numbers together, and all the variables
8x+4x.5(x-12)-(12x-9)=0
We multiply parentheses
4x^2+8x-48x-(12x-9)=0
We get rid of parentheses
4x^2+8x-48x-12x+9=0
We add all the numbers together, and all the variables
4x^2-52x+9=0
a = 4; b = -52; c = +9;
Δ = b2-4ac
Δ = -522-4·4·9
Δ = 2560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-16\sqrt{10}}{2*4}=\frac{52-16\sqrt{10}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+16\sqrt{10}}{2*4}=\frac{52+16\sqrt{10}}{8} $
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