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(2x+1)(4x-7)=0
We multiply parentheses ..
(+8x^2-14x+4x-7)=0
We get rid of parentheses
8x^2-14x+4x-7=0
We add all the numbers together, and all the variables
8x^2-10x-7=0
a = 8; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·8·(-7)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18}{2*8}=\frac{-8}{16} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18}{2*8}=\frac{28}{16} =1+3/4 $
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