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(6x-7)(4x=23)
We move all terms to the left:
(6x-7)(4x-(23))=0
We multiply parentheses ..
(+24x^2-138x-28x+161)=0
We get rid of parentheses
24x^2-138x-28x+161=0
We add all the numbers together, and all the variables
24x^2-166x+161=0
a = 24; b = -166; c = +161;
Δ = b2-4ac
Δ = -1662-4·24·161
Δ = 12100
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{12100}=110$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-110}{2*24}=\frac{56}{48} =1+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+110}{2*24}=\frac{276}{48} =5+3/4 $
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