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6x(x+7)=7x+49
We move all terms to the left:
6x(x+7)-(7x+49)=0
We multiply parentheses
6x^2+42x-(7x+49)=0
We get rid of parentheses
6x^2+42x-7x-49=0
We add all the numbers together, and all the variables
6x^2+35x-49=0
a = 6; b = 35; c = -49;
Δ = b2-4ac
Δ = 352-4·6·(-49)
Δ = 2401
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{2401}=49$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-49}{2*6}=\frac{-84}{12} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+49}{2*6}=\frac{14}{12} =1+1/6 $
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