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(2x-3)x-52=0
We multiply parentheses
2x^2-3x-52=0
a = 2; b = -3; c = -52;
Δ = b2-4ac
Δ = -32-4·2·(-52)
Δ = 425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5\sqrt{17}}{2*2}=\frac{3-5\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5\sqrt{17}}{2*2}=\frac{3+5\sqrt{17}}{4} $
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