10x^2-5x+7=15

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Solution for 10x^2-5x+7=15 equation:



10x^2-5x+7=15
We move all terms to the left:
10x^2-5x+7-(15)=0
We add all the numbers together, and all the variables
10x^2-5x-8=0
a = 10; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·10·(-8)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{345}}{2*10}=\frac{5-\sqrt{345}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*10}=\frac{5+\sqrt{345}}{20} $

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