75a^2+8513a-693634=0

Solution for 75a^2+8513a-693634=0 equation:

75a^2+8513a-693634=0

a = 75; b = 8513; c = -693634;
Δ = b2-4ac
Δ = 85132-4·75·(-693634)
Δ = 280561369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280561369}=\sqrt{121*2318689}=\sqrt{121}*\sqrt{2318689}=11\sqrt{2318689}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8513)-11\sqrt{2318689}}{2*75}=\frac{-8513-11\sqrt{2318689}}{150}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8513)+11\sqrt{2318689}}{2*75}=\frac{-8513+11\sqrt{2318689}}{150}
$