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3x^2=8x+13
We move all terms to the left:
3x^2-(8x+13)=0
We get rid of parentheses
3x^2-8x-13=0
a = 3; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·3·(-13)
Δ = 220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{55}}{2*3}=\frac{8-2\sqrt{55}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{55}}{2*3}=\frac{8+2\sqrt{55}}{6} $
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