8x^2-13x=-3/2

Solution for 8x^2-13x=-3/2 equation:

8x^2-13x=-3/2

We move all terms to the left:

8x^2-13x-(-3/2)=0

We get rid of parentheses

8x^2-13x+3/2=0

We multiply all the terms by the denominator


8x^2*2-13x*2+3=0

Wy multiply elements

16x^2-26x+3=0

a = 16; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·16·3
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*16}=\frac{4}{32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*16}=\frac{48}{32}
=1+1/2
$