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5x^2=7x+7
We move all terms to the left:
5x^2-(7x+7)=0
We get rid of parentheses
5x^2-7x-7=0
a = 5; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·5·(-7)
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{21}}{2*5}=\frac{7-3\sqrt{21}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{21}}{2*5}=\frac{7+3\sqrt{21}}{10} $
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