2x^2-9x+7=75

Solution for 2x^2-9x+7=75 equation:

2x^2-9x+7=75

We move all terms to the left:

2x^2-9x+7-(75)=0

We add all the numbers together, and all the variables

2x^2-9x-68=0

a = 2; b = -9; c = -68;
Δ = b2-4ac
Δ = -92-4·2·(-68)
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{-(-9)-25}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+25}{2*2}=\frac{34}{4}
=8+1/2
$