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-12x^2-4x+18=3x-7
We move all terms to the left:
-12x^2-4x+18-(3x-7)=0
We get rid of parentheses
-12x^2-4x-3x+7+18=0
We add all the numbers together, and all the variables
-12x^2-7x+25=0
a = -12; b = -7; c = +25;
Δ = b2-4ac
Δ = -72-4·(-12)·25
Δ = 1249
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{-(-7)-\sqrt{1249}}{2*-12}=\frac{7-\sqrt{1249}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1249}}{2*-12}=\frac{7+\sqrt{1249}}{-24} $
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