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(4x+1)(6x-7)=0
We multiply parentheses ..
(+24x^2-28x+6x-7)=0
We get rid of parentheses
24x^2-28x+6x-7=0
We add all the numbers together, and all the variables
24x^2-22x-7=0
a = 24; b = -22; c = -7;
Δ = b2-4ac
Δ = -222-4·24·(-7)
Δ = 1156
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{1156}=34$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-34}{2*24}=\frac{-12}{48} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+34}{2*24}=\frac{56}{48} =1+1/6 $
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