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(4x-5)(6x=2)
We move all terms to the left:
(4x-5)(6x-(2))=0
We multiply parentheses ..
(+24x^2-8x-30x+10)=0
We get rid of parentheses
24x^2-8x-30x+10=0
We add all the numbers together, and all the variables
24x^2-38x+10=0
a = 24; b = -38; c = +10;
Δ = b2-4ac
Δ = -382-4·24·10
Δ = 484
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{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22}{2*24}=\frac{16}{48} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22}{2*24}=\frac{60}{48} =1+1/4 $
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