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-7x-5=-7x^2
We move all terms to the left:
-7x-5-(-7x^2)=0
We get rid of parentheses
7x^2-7x-5=0
a = 7; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·7·(-5)
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*7}=\frac{7-3\sqrt{21}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{21}}{2*7}=\frac{7+3\sqrt{21}}{14} $
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