2x^2+2.5x+1.5=69

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Solution for 2x^2+2.5x+1.5=69 equation:



2x^2+2.5x+1.5=69
We move all terms to the left:
2x^2+2.5x+1.5-(69)=0
We add all the numbers together, and all the variables
2x^2+2.5x-67.5=0
a = 2; b = 2.5; c = -67.5;
Δ = b2-4ac
Δ = 2.52-4·2·(-67.5)
Δ = 546.25
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{-(2.5)-\sqrt{546.25}}{2*2}=\frac{-2.5-\sqrt{546.25}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{546.25}}{2*2}=\frac{-2.5+\sqrt{546.25}}{4} $

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