5x^2+3=x^2-7x

Solution for 5x^2+3=x^2-7x equation:

5x^2+3=x^2-7x

We move all terms to the left:

5x^2+3-(x^2-7x)=0

We get rid of parentheses

5x^2-x^2+7x+3=0

We add all the numbers together, and all the variables

4x^2+7x+3=0

a = 4; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·4·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*4}=\frac{-6}{8}
=-3/4
$