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6x^2+5x+3=6x+5
We move all terms to the left:
6x^2+5x+3-(6x+5)=0
We get rid of parentheses
6x^2+5x-6x-5+3=0
We add all the numbers together, and all the variables
6x^2-1x-2=0
a = 6; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·6·(-2)
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*6}=\frac{-6}{12} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*6}=\frac{8}{12} =2/3 $
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