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6x^2+3x-5=2
We move all terms to the left:
6x^2+3x-5-(2)=0
We add all the numbers together, and all the variables
6x^2+3x-7=0
a = 6; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·6·(-7)
Δ = 177
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{177}}{2*6}=\frac{-3-\sqrt{177}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{177}}{2*6}=\frac{-3+\sqrt{177}}{12} $
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