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21z^2+85z-25=0
a = 21; b = 85; c = -25;
Δ = b2-4ac
Δ = 852-4·21·(-25)
Δ = 9325
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9325}=\sqrt{25*373}=\sqrt{25}*\sqrt{373}=5\sqrt{373}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-5\sqrt{373}}{2*21}=\frac{-85-5\sqrt{373}}{42} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+5\sqrt{373}}{2*21}=\frac{-85+5\sqrt{373}}{42} $
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