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7x^2+10=2x+9x^2
We move all terms to the left:
7x^2+10-(2x+9x^2)=0
We get rid of parentheses
7x^2-9x^2-2x+10=0
We add all the numbers together, and all the variables
-2x^2-2x+10=0
a = -2; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-2)·10
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*-2}=\frac{2-2\sqrt{21}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*-2}=\frac{2+2\sqrt{21}}{-4} $
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