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7x^2+6x-37500=0
a = 7; b = 6; c = -37500;
Δ = b2-4ac
Δ = 62-4·7·(-37500)
Δ = 1050036
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1050036}=\sqrt{4*262509}=\sqrt{4}*\sqrt{262509}=2\sqrt{262509}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{262509}}{2*7}=\frac{-6-2\sqrt{262509}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{262509}}{2*7}=\frac{-6+2\sqrt{262509}}{14} $
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