5x+1=3.5x2

Solution for 5x+1=3.5x2 equation:

5x+1=3.5x^2

We move all terms to the left:

5x+1-(3.5x^2)=0

We get rid of parentheses

-3.5x^2+5x+1=0

a = -3.5; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-3.5)·1
Δ = 39
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{39}}{2*-3.5}=\frac{-5-\sqrt{39}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{39}}{2*-3.5}=\frac{-5+\sqrt{39}}{-7}
$