2x(x+5)=3x+5

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Solution for 2x(x+5)=3x+5 equation:



2x(x+5)=3x+5
We move all terms to the left:
2x(x+5)-(3x+5)=0
We multiply parentheses
2x^2+10x-(3x+5)=0
We get rid of parentheses
2x^2+10x-3x-5=0
We add all the numbers together, and all the variables
2x^2+7x-5=0
a = 2; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·2·(-5)
Δ = 89
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{89}}{2*2}=\frac{-7-\sqrt{89}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{89}}{2*2}=\frac{-7+\sqrt{89}}{4} $

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