2x^2-3=x(x+5)-3

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

2x^2-3=x(x+5)-3

We move all terms to the left:

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


We calculate terms in parentheses: -(x(x+5)-3), so:

x(x+5)-3

We multiply parentheses

x^2+5x-3

Back to the equation:

-(x^2+5x-3)


We get rid of parentheses

2x^2-x^2-5x+3-3=0

We add all the numbers together, and all the variables

x^2-5x=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$