8x^2=30x+42

Solution for 8x^2=30x+42 equation:

8x^2=30x+42

We move all terms to the left:

8x^2-(30x+42)=0

We get rid of parentheses

8x^2-30x-42=0

a = 8; b = -30; c = -42;
Δ = b2-4ac
Δ = -302-4·8·(-42)
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{561}}{2*8}=\frac{30-2\sqrt{561}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{561}}{2*8}=\frac{30+2\sqrt{561}}{16}
$