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12x-10x=8x^2-3x^2
We move all terms to the left:
12x-10x-(8x^2-3x^2)=0
We add all the numbers together, and all the variables
-(8x^2-3x^2)+2x=0
We get rid of parentheses
-8x^2+3x^2+2x=0
We add all the numbers together, and all the variables
-5x^2+2x=0
a = -5; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-5)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-5}=\frac{-4}{-10} =2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-5}=\frac{0}{-10} =0 $
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