3+x(2x-5)=78

Solution for 3+x(2x-5)=78 equation:

3+x(2x-5)=78

We move all terms to the left:

3+x(2x-5)-(78)=0

We add all the numbers together, and all the variables

x(2x-5)-75=0

We multiply parentheses

2x^2-5x-75=0

a = 2; b = -5; c = -75;
Δ = b2-4ac
Δ = -52-4·2·(-75)
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{-(-5)-25}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*2}=\frac{30}{4}
=7+1/2
$