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6z+5(-2z-7)z=-1
We move all terms to the left:
6z+5(-2z-7)z-(-1)=0
We add all the numbers together, and all the variables
6z+5(-2z-7)z+1=0
We multiply parentheses
-10z^2+6z-35z+1=0
We add all the numbers together, and all the variables
-10z^2-29z+1=0
a = -10; b = -29; c = +1;
Δ = b2-4ac
Δ = -292-4·(-10)·1
Δ = 881
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{881}}{2*-10}=\frac{29-\sqrt{881}}{-20} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{881}}{2*-10}=\frac{29+\sqrt{881}}{-20} $
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