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13x^2-5x=6-12x^2
We move all terms to the left:
13x^2-5x-(6-12x^2)=0
We get rid of parentheses
13x^2+12x^2-5x-6=0
We add all the numbers together, and all the variables
25x^2-5x-6=0
a = 25; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·25·(-6)
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*25}=\frac{-20}{50} =-2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*25}=\frac{30}{50} =3/5 $
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