4x2-18x=15

Solution for 4x2-18x=15 equation:

4x^2-18x=15

We move all terms to the left:

4x^2-18x-(15)=0

a = 4; b = -18; c = -15;
Δ = b2-4ac
Δ = -182-4·4·(-15)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{141}}{2*4}=\frac{18-2\sqrt{141}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{141}}{2*4}=\frac{18+2\sqrt{141}}{8}
$