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3x+30+x=10+2x+5x^2
We move all terms to the left:
3x+30+x-(10+2x+5x^2)=0
We add all the numbers together, and all the variables
-(10+2x+5x^2)+4x+30=0
We get rid of parentheses
-5x^2-2x+4x-10+30=0
We add all the numbers together, and all the variables
-5x^2+2x+20=0
a = -5; b = 2; c = +20;
Δ = b2-4ac
Δ = 22-4·(-5)·20
Δ = 404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{101}}{2*-5}=\frac{-2-2\sqrt{101}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{101}}{2*-5}=\frac{-2+2\sqrt{101}}{-10} $
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