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(-9z+2)(-5z-7)=0
We multiply parentheses ..
(+45z^2+63z-10z-14)=0
We get rid of parentheses
45z^2+63z-10z-14=0
We add all the numbers together, and all the variables
45z^2+53z-14=0
a = 45; b = 53; c = -14;
Δ = b2-4ac
Δ = 532-4·45·(-14)
Δ = 5329
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{5329}=73$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-73}{2*45}=\frac{-126}{90} =-1+2/5 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+73}{2*45}=\frac{20}{90} =2/9 $
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