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12x^2+2x-5=8
We move all terms to the left:
12x^2+2x-5-(8)=0
We add all the numbers together, and all the variables
12x^2+2x-13=0
a = 12; b = 2; c = -13;
Δ = b2-4ac
Δ = 22-4·12·(-13)
Δ = 628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{157}}{2*12}=\frac{-2-2\sqrt{157}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{157}}{2*12}=\frac{-2+2\sqrt{157}}{24} $
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