7x^2+8x-9=10

Solution for 7x^2+8x-9=10 equation:

7x^2+8x-9=10

We move all terms to the left:

7x^2+8x-9-(10)=0

We add all the numbers together, and all the variables

7x^2+8x-19=0

a = 7; b = 8; c = -19;
Δ = b2-4ac
Δ = 82-4·7·(-19)
Δ = 596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{149}}{2*7}=\frac{-8-2\sqrt{149}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{149}}{2*7}=\frac{-8+2\sqrt{149}}{14}
$