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(6x+7)(4x-5)=0
We multiply parentheses ..
(+24x^2-30x+28x-35)=0
We get rid of parentheses
24x^2-30x+28x-35=0
We add all the numbers together, and all the variables
24x^2-2x-35=0
a = 24; b = -2; c = -35;
Δ = b2-4ac
Δ = -22-4·24·(-35)
Δ = 3364
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{3364}=58$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-58}{2*24}=\frac{-56}{48} =-1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+58}{2*24}=\frac{60}{48} =1+1/4 $
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