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6x^2+43x=-42
We move all terms to the left:
6x^2+43x-(-42)=0
We add all the numbers together, and all the variables
6x^2+43x+42=0
a = 6; b = 43; c = +42;
Δ = b2-4ac
Δ = 432-4·6·42
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-29}{2*6}=\frac{-72}{12} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+29}{2*6}=\frac{-14}{12} =-1+1/6 $
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