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7x^2=8x+11
We move all terms to the left:
7x^2-(8x+11)=0
We get rid of parentheses
7x^2-8x-11=0
a = 7; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·7·(-11)
Δ = 372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{93}}{2*7}=\frac{8-2\sqrt{93}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{93}}{2*7}=\frac{8+2\sqrt{93}}{14} $
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