x^2=-7x-3/2

Solution for x^2=-7x-3/2 equation:

x^2=-7x-3/2

We move all terms to the left:

x^2-(-7x-3/2)=0

We get rid of parentheses

x^2+7x+3/2=0

We multiply all the terms by the denominator


x^2*2+7x*2+3=0

Wy multiply elements

2x^2+14x+3=0

a = 2; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·2·3
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{43}}{2*2}=\frac{-14-2\sqrt{43}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{43}}{2*2}=\frac{-14+2\sqrt{43}}{4}
$