-5u^2-12u+24=-2u+15

Solution for -5u^2-12u+24=-2u+15 equation:

-5u^2-12u+24=-2u+15

We move all terms to the left:

-5u^2-12u+24-(-2u+15)=0

We get rid of parentheses

-5u^2-12u+2u-15+24=0

We add all the numbers together, and all the variables

-5u^2-10u+9=0

a = -5; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·(-5)·9
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*-5}=\frac{10-2\sqrt{70}}{-10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*-5}=\frac{10+2\sqrt{70}}{-10}
$