10-7x^2=-3x+5

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Solution for 10-7x^2=-3x+5 equation:



10-7x^2=-3x+5
We move all terms to the left:
10-7x^2-(-3x+5)=0
We get rid of parentheses
-7x^2+3x-5+10=0
We add all the numbers together, and all the variables
-7x^2+3x+5=0
a = -7; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-7)·5
Δ = 149
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{-(3)-\sqrt{149}}{2*-7}=\frac{-3-\sqrt{149}}{-14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*-7}=\frac{-3+\sqrt{149}}{-14} $

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