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x(6x-19)=-8
We move all terms to the left:
x(6x-19)-(-8)=0
We add all the numbers together, and all the variables
x(6x-19)+8=0
We multiply parentheses
6x^2-19x+8=0
a = 6; b = -19; c = +8;
Δ = b2-4ac
Δ = -192-4·6·8
Δ = 169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-13}{2*6}=\frac{6}{12} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+13}{2*6}=\frac{32}{12} =2+2/3 $
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