7x^2=-5x+9

Solution for 7x^2=-5x+9 equation:

7x^2=-5x+9

We move all terms to the left:

7x^2-(-5x+9)=0

We get rid of parentheses

7x^2+5x-9=0

a = 7; b = 5; c = -9;
Δ = b2-4ac
Δ = 52-4·7·(-9)
Δ = 277
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{277}}{2*7}=\frac{-5-\sqrt{277}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{277}}{2*7}=\frac{-5+\sqrt{277}}{14}
$