(5x)=3x^2-7

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

(5x)=3x^2-7

We move all terms to the left:

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

We get rid of parentheses

-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}
$