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x(5x-3)=7
We move all terms to the left:
x(5x-3)-(7)=0
We multiply parentheses
5x^2-3x-7=0
a = 5; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·5·(-7)
Δ = 149
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{149}}{2*5}=\frac{3-\sqrt{149}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{149}}{2*5}=\frac{3+\sqrt{149}}{10} $
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