8(x2-5)=7x+2

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Solution for 8(x2-5)=7x+2 equation:



8(x2-5)=7x+2
We move all terms to the left:
8(x2-5)-(7x+2)=0
We add all the numbers together, and all the variables
8(+x^2-5)-(7x+2)=0
We multiply parentheses
8x^2-(7x+2)-40=0
We get rid of parentheses
8x^2-7x-2-40=0
We add all the numbers together, and all the variables
8x^2-7x-42=0
a = 8; b = -7; c = -42;
Δ = b2-4ac
Δ = -72-4·8·(-42)
Δ = 1393
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{-(-7)-\sqrt{1393}}{2*8}=\frac{7-\sqrt{1393}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1393}}{2*8}=\frac{7+\sqrt{1393}}{16} $

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