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x(5x-2)=52
We move all terms to the left:
x(5x-2)-(52)=0
We multiply parentheses
5x^2-2x-52=0
a = 5; b = -2; c = -52;
Δ = b2-4ac
Δ = -22-4·5·(-52)
Δ = 1044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{29}}{2*5}=\frac{2-6\sqrt{29}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{29}}{2*5}=\frac{2+6\sqrt{29}}{10} $
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