4x2+7x=8

Solution for 4x2+7x=8 equation:

4x^2+7x=8

We move all terms to the left:

4x^2+7x-(8)=0

a = 4; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·4·(-8)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{177}}{2*4}=\frac{-7-\sqrt{177}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{177}}{2*4}=\frac{-7+\sqrt{177}}{8}
$