7x^2-9x=10

Solution for 7x^2-9x=10 equation:

7x^2-9x=10

We move all terms to the left:

7x^2-9x-(10)=0

a = 7; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·7·(-10)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*7}=\frac{28}{14}
=2
$