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12x^2-10x+7x-3=22
We move all terms to the left:
12x^2-10x+7x-3-(22)=0
We add all the numbers together, and all the variables
12x^2-3x-25=0
a = 12; b = -3; c = -25;
Δ = b2-4ac
Δ = -32-4·12·(-25)
Δ = 1209
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1209}}{2*12}=\frac{3-\sqrt{1209}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1209}}{2*12}=\frac{3+\sqrt{1209}}{24} $
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