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7x=6x^2-3
We move all terms to the left:
7x-(6x^2-3)=0
We get rid of parentheses
-6x^2+7x+3=0
a = -6; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-6)·3
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-6}=\frac{-18}{-12} =1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-6}=\frac{4}{-12} =-1/3 $
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