7=2x^2+5x-3

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

7=2x^2+5x-3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-5x+10=0

a = -2; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-2)·10
Δ = 105
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{-(-5)-\sqrt{105}}{2*-2}=\frac{5-\sqrt{105}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*-2}=\frac{5+\sqrt{105}}{-4}
$