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105x^2-276x+75=0
a = 105; b = -276; c = +75;
Δ = b2-4ac
Δ = -2762-4·105·75
Δ = 44676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44676}=\sqrt{36*1241}=\sqrt{36}*\sqrt{1241}=6\sqrt{1241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-6\sqrt{1241}}{2*105}=\frac{276-6\sqrt{1241}}{210} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+6\sqrt{1241}}{2*105}=\frac{276+6\sqrt{1241}}{210} $
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