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-2x(5x-8)+6x/4=x-8
We move all terms to the left:
-2x(5x-8)+6x/4-(x-8)=0
We multiply parentheses
-10x^2+16x+6x/4-(x-8)=0
We get rid of parentheses
-10x^2+16x+6x/4-x+8=0
We multiply all the terms by the denominator
-10x^2*4+16x*4+6x-x*4+8*4=0
We add all the numbers together, and all the variables
-10x^2*4+6x+16x*4-x*4+32=0
Wy multiply elements
-40x^2+6x+64x-4x+32=0
We add all the numbers together, and all the variables
-40x^2+66x+32=0
a = -40; b = 66; c = +32;
Δ = b2-4ac
Δ = 662-4·(-40)·32
Δ = 9476
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9476}=\sqrt{4*2369}=\sqrt{4}*\sqrt{2369}=2\sqrt{2369}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{2369}}{2*-40}=\frac{-66-2\sqrt{2369}}{-80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{2369}}{2*-40}=\frac{-66+2\sqrt{2369}}{-80} $
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