2x2+10x=75+x2

Solution for 2x2+10x=75+x2 equation:

2x^2+10x=75+x2

We move all terms to the left:

2x^2+10x-(75+x2)=0

We add all the numbers together, and all the variables

2x^2-(+x^2+75)+10x=0

We get rid of parentheses

2x^2-x^2+10x-75=0

We add all the numbers together, and all the variables

x^2+10x-75=0

a = 1; b = 10; c = -75;
Δ = b2-4ac
Δ = 102-4·1·(-75)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*1}=\frac{10}{2}
=5
$