14x^2+31x+15=0*

Solution for 14x^2+31x+15=0* equation:

14x^2+31x+15=0*

We move all terms to the left:

14x^2+31x+15-(0*)=0

We add all the numbers together, and all the variables

14x^2+31x+15-0=0

We add all the numbers together, and all the variables

14x^2+31x+15=0

a = 14; b = 31; c = +15;
Δ = b2-4ac
Δ = 312-4·14·15
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-11}{2*14}=\frac{-42}{28}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+11}{2*14}=\frac{-20}{28}
=-5/7
$