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(4x+1)(2x+7)=0
We multiply parentheses ..
(+8x^2+28x+2x+7)=0
We get rid of parentheses
8x^2+28x+2x+7=0
We add all the numbers together, and all the variables
8x^2+30x+7=0
a = 8; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·8·7
Δ = 676
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{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-26}{2*8}=\frac{-56}{16} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+26}{2*8}=\frac{-4}{16} =-1/4 $
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