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5x+8=9x+12x^2
We move all terms to the left:
5x+8-(9x+12x^2)=0
We get rid of parentheses
-12x^2-9x+5x+8=0
We add all the numbers together, and all the variables
-12x^2-4x+8=0
a = -12; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-12)·8
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-12}=\frac{-16}{-24} =2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-12}=\frac{24}{-24} =-1 $
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