12x^2=5+10x

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Solution for 12x^2=5+10x equation:



12x^2=5+10x
We move all terms to the left:
12x^2-(5+10x)=0
We add all the numbers together, and all the variables
12x^2-(10x+5)=0
We get rid of parentheses
12x^2-10x-5=0
a = 12; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·12·(-5)
Δ = 340
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:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*12}=\frac{10-2\sqrt{85}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*12}=\frac{10+2\sqrt{85}}{24} $

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