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(2z+7)(4z-10)=0
We multiply parentheses ..
(+8z^2-20z+28z-70)=0
We get rid of parentheses
8z^2-20z+28z-70=0
We add all the numbers together, and all the variables
8z^2+8z-70=0
a = 8; b = 8; c = -70;
Δ = b2-4ac
Δ = 82-4·8·(-70)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2304}=48$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-48}{2*8}=\frac{-56}{16} =-3+1/2 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+48}{2*8}=\frac{40}{16} =2+1/2 $
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