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3x^2+2-7=2x+5
We move all terms to the left:
3x^2+2-7-(2x+5)=0
We add all the numbers together, and all the variables
3x^2-(2x+5)-5=0
We get rid of parentheses
3x^2-2x-5-5=0
We add all the numbers together, and all the variables
3x^2-2x-10=0
a = 3; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·3·(-10)
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*3}=\frac{2-2\sqrt{31}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*3}=\frac{2+2\sqrt{31}}{6} $
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