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-5x-3x(-2x-13)=47
We move all terms to the left:
-5x-3x(-2x-13)-(47)=0
We multiply parentheses
6x^2-5x+39x-47=0
We add all the numbers together, and all the variables
6x^2+34x-47=0
a = 6; b = 34; c = -47;
Δ = b2-4ac
Δ = 342-4·6·(-47)
Δ = 2284
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2284}=\sqrt{4*571}=\sqrt{4}*\sqrt{571}=2\sqrt{571}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{571}}{2*6}=\frac{-34-2\sqrt{571}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{571}}{2*6}=\frac{-34+2\sqrt{571}}{12} $
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