2x^2+7x-5=67

Solution for 2x^2+7x-5=67 equation:

2x^2+7x-5=67

We move all terms to the left:

2x^2+7x-5-(67)=0

We add all the numbers together, and all the variables

2x^2+7x-72=0

a = 2; b = 7; c = -72;
Δ = b2-4ac
Δ = 72-4·2·(-72)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*2}=\frac{18}{4}
=4+1/2
$