2*x*x-3=7x+3

Solution for 2*x*x-3=7x+3 equation:

2x*x-3=7x+3

We move all terms to the left:

2x*x-3-(7x+3)=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-7x-6=0

a = 2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·2·(-6)
Δ = 97
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{97}}{2*2}=\frac{7-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*2}=\frac{7+\sqrt{97}}{4}
$