x2+3x+5=75

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Solution for x2+3x+5=75 equation:



x2+3x+5=75
We move all terms to the left:
x2+3x+5-(75)=0
We add all the numbers together, and all the variables
x^2+3x-70=0
a = 1; b = 3; c = -70;
Δ = b2-4ac
Δ = 32-4·1·(-70)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*1}=\frac{-20}{2} =-10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*1}=\frac{14}{2} =7 $

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