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228=8x^2+6x-2
We move all terms to the left:
228-(8x^2+6x-2)=0
We get rid of parentheses
-8x^2-6x+2+228=0
We add all the numbers together, and all the variables
-8x^2-6x+230=0
a = -8; b = -6; c = +230;
Δ = b2-4ac
Δ = -62-4·(-8)·230
Δ = 7396
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{7396}=86$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-86}{2*-8}=\frac{-80}{-16} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+86}{2*-8}=\frac{92}{-16} =-5+3/4 $
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