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6x-2x^2=3x+5x^2
We move all terms to the left:
6x-2x^2-(3x+5x^2)=0
We get rid of parentheses
-2x^2-5x^2-3x+6x=0
We add all the numbers together, and all the variables
-7x^2+3x=0
a = -7; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-7)·0
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-7}=\frac{-6}{-14} =3/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-7}=\frac{0}{-14} =0 $
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