(4s^2-2s-3)-(5s^2+7s-6)=0

Solution for (4s^2-2s-3)-(5s^2+7s-6)=0 equation:

(4s^2-2s-3)-(5s^2+7s-6)=0

We get rid of parentheses

4s^2-5s^2-2s-7s-3+6=0

We add all the numbers together, and all the variables

-1s^2-9s+3=0

a = -1; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-1)·3
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{93}}{2*-1}=\frac{9-\sqrt{93}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*-1}=\frac{9+\sqrt{93}}{-2}
$