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5x^2+3x-7=12x+12
We move all terms to the left:
5x^2+3x-7-(12x+12)=0
We get rid of parentheses
5x^2+3x-12x-12-7=0
We add all the numbers together, and all the variables
5x^2-9x-19=0
a = 5; b = -9; c = -19;
Δ = b2-4ac
Δ = -92-4·5·(-19)
Δ = 461
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{-(-9)-\sqrt{461}}{2*5}=\frac{9-\sqrt{461}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{461}}{2*5}=\frac{9+\sqrt{461}}{10} $
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