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7x^2=-18x-4
We move all terms to the left:
7x^2-(-18x-4)=0
We get rid of parentheses
7x^2+18x+4=0
a = 7; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·7·4
Δ = 212
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{53}}{2*7}=\frac{-18-2\sqrt{53}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{53}}{2*7}=\frac{-18+2\sqrt{53}}{14} $
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