7x^2+2x-15=57-53x

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Solution for 7x^2+2x-15=57-53x equation:



7x^2+2x-15=57-53x
We move all terms to the left:
7x^2+2x-15-(57-53x)=0
We add all the numbers together, and all the variables
7x^2+2x-(-53x+57)-15=0
We get rid of parentheses
7x^2+2x+53x-57-15=0
We add all the numbers together, and all the variables
7x^2+55x-72=0
a = 7; b = 55; c = -72;
Δ = b2-4ac
Δ = 552-4·7·(-72)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-71}{2*7}=\frac{-126}{14} =-9 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+71}{2*7}=\frac{16}{14} =1+1/7 $

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