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

Solution for 2(x^2+3/2x-7)=0 equation:

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


Domain of the equation: 2x-7)!=0

x∈R


We multiply parentheses

2x^2+6x-14=0

a = 2; b = 6; c = -14;
Δ = b2-4ac
Δ = 62-4·2·(-14)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*2}=\frac{-6-2\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*2}=\frac{-6+2\sqrt{37}}{4}
$