4u^2=21u-18

Solution for 4u^2=21u-18 equation:

4u^2=21u-18

We move all terms to the left:

4u^2-(21u-18)=0

We get rid of parentheses

4u^2-21u+18=0

a = 4; b = -21; c = +18;
Δ = b2-4ac
Δ = -212-4·4·18
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{17}}{2*4}=\frac{21-3\sqrt{17}}{8}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*4}=\frac{21+3\sqrt{17}}{8}
$