7-5x=3x2

Solution for 7-5x=3x2 equation:

7-5x=3x^2

We move all terms to the left:

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

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

a = -3; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-3)·7
Δ = 109
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{109}}{2*-3}=\frac{5-\sqrt{109}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*-3}=\frac{5+\sqrt{109}}{-6}
$