5x^2=7x+66

Solution for 5x^2=7x+66 equation:

5x^2=7x+66

We move all terms to the left:

5x^2-(7x+66)=0

We get rid of parentheses

5x^2-7x-66=0

a = 5; b = -7; c = -66;
Δ = b2-4ac
Δ = -72-4·5·(-66)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*5}=\frac{44}{10}
=4+2/5
$