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75=6x^2
We move all terms to the left:
75-(6x^2)=0
a = -6; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-6)·75
Δ = 1800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*-6}=\frac{0-30\sqrt{2}}{-12} =-\frac{30\sqrt{2}}{-12} =-\frac{5\sqrt{2}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*-6}=\frac{0+30\sqrt{2}}{-12} =\frac{30\sqrt{2}}{-12} =\frac{5\sqrt{2}}{-2} $
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