5x+78=2x*x+24

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Solution for 5x+78=2x*x+24 equation:



5x+78=2x*x+24
We move all terms to the left:
5x+78-(2x*x+24)=0
We get rid of parentheses
5x-2x*x-24+78=0
We add all the numbers together, and all the variables
5x-2x*x+54=0
Wy multiply elements
-2x^2+5x+54=0
a = -2; b = 5; c = +54;
Δ = b2-4ac
Δ = 52-4·(-2)·54
Δ = 457
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{457}}{2*-2}=\frac{-5-\sqrt{457}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{457}}{2*-2}=\frac{-5+\sqrt{457}}{-4} $

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