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(3x-8)(8x-7)=0
We multiply parentheses ..
(+24x^2-21x-64x+56)=0
We get rid of parentheses
24x^2-21x-64x+56=0
We add all the numbers together, and all the variables
24x^2-85x+56=0
a = 24; b = -85; c = +56;
Δ = b2-4ac
Δ = -852-4·24·56
Δ = 1849
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1849}=43$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-43}{2*24}=\frac{42}{48} =7/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+43}{2*24}=\frac{128}{48} =2+2/3 $
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