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(x)(2x+1)=6x+7
We move all terms to the left:
(x)(2x+1)-(6x+7)=0
We multiply parentheses
2x^2+x-(6x+7)=0
We get rid of parentheses
2x^2+x-6x-7=0
We add all the numbers together, and all the variables
2x^2-5x-7=0
a = 2; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·2·(-7)
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*2}=\frac{-4}{4} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*2}=\frac{14}{4} =3+1/2 $
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