4x^2-3=x^2-7x

Solution for 4x^2-3=x^2-7x equation:

4x^2-3=x^2-7x

We move all terms to the left:

4x^2-3-(x^2-7x)=0

We get rid of parentheses

4x^2-x^2+7x-3=0

We add all the numbers together, and all the variables

3x^2+7x-3=0

a = 3; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·3·(-3)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{85}}{2*3}=\frac{-7-\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*3}=\frac{-7+\sqrt{85}}{6}
$