2x^2-7x-4=45

Solution for 2x^2-7x-4=45 equation:

2x^2-7x-4=45

We move all terms to the left:

2x^2-7x-4-(45)=0

We add all the numbers together, and all the variables

2x^2-7x-49=0

a = 2; b = -7; c = -49;
Δ = b2-4ac
Δ = -72-4·2·(-49)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-21}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+21}{2*2}=\frac{28}{4}
=7
$